{"id":231,"date":"2023-08-03T20:48:38","date_gmt":"2023-08-03T20:48:38","guid":{"rendered":"https:\/\/statorials.org\/ar\/%d8%a7%d9%84%d8%aa%d9%88%d8%b2%d9%8a%d8%b9-%d8%b0%d9%88-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-1\/"},"modified":"2023-08-03T20:48:38","modified_gmt":"2023-08-03T20:48:38","slug":"%d8%a7%d9%84%d8%aa%d9%88%d8%b2%d9%8a%d8%b9-%d8%b0%d9%88-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/%d8%a7%d9%84%d8%aa%d9%88%d8%b2%d9%8a%d8%b9-%d8%b0%d9%88-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-1\/","title":{"rendered":"\u062a\u0648\u0632\u064a\u0639 \u062b\u0646\u0627\u0626\u064a"},"content":{"rendered":"

\u062a\u0634\u0631\u062d \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u0627\u0647\u064a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0627\u062a \u0648\u0641\u064a\u0645 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647. \u0648\u0644\u0630\u0644\u0643 \u0633\u062a\u062c\u062f \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u0648\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0648\u062e\u0635\u0627\u0626\u0635 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u0648\u0641 \u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u062d\u0633\u0627\u0628 \u0623\u064a \u0627\u062d\u062a\u0645\u0627\u0644 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a. <\/p>\n

<\/span> \u0645\u0627 \u0647\u0648 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646\u061f<\/span><\/h2>\n

\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646<\/strong> \u0647\u0648 \u062a\u0648\u0632\u064a\u0639 \u0627\u062d\u062a\u0645\u0627\u0644\u064a \u064a\u062d\u0633\u0628 \u0639\u062f\u062f \u0627\u0644\u0646\u062c\u0627\u062d\u0627\u062a \u0639\u0646\u062f \u0625\u062c\u0631\u0627\u0621 \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062a\u062c\u0627\u0631\u0628 \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0645\u0639 \u0627\u062d\u062a\u0645\u0627\u0644 \u062b\u0627\u0628\u062a \u0644\u0644\u0646\u062c\u0627\u062d.<\/p>\n

\u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u0647\u0648 \u062a\u0648\u0632\u064a\u0639 \u064a\u0635\u0641 \u0639\u062f\u062f \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0646\u0627\u062c\u062d\u0629 \u0644\u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u062a\u062c\u0627\u0631\u0628 \u0628\u0631\u0646\u0648\u0644\u064a.<\/p>\n

\u062a\u0630\u0643\u0631 \u0623\u0646 \u0627\u062e\u062a\u0628\u0627\u0631 \u0628\u0631\u0646\u0648\u0644\u064a \u0647\u0648 \u062a\u062c\u0631\u0628\u0629 \u0644\u0647\u0627 \u0646\u062a\u064a\u062c\u062a\u0627\u0646 \u0645\u062d\u062a\u0645\u0644\u062a\u0627\u0646: “\u0627\u0644\u0646\u062c\u0627\u062d” \u0648”\u0627\u0644\u0641\u0634\u0644”. \u0644\u0630\u0644\u0643\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u062d\u062a\u0645\u0627\u0644 “\u0627\u0644\u0646\u062c\u0627\u062d” \u0647\u0648 p<\/em> \u060c \u0641\u0625\u0646 \u0627\u062d\u062a\u0645\u0627\u0644 “\u0627\u0644\u0641\u0634\u0644” \u0647\u0648 q=1-p<\/em> .<\/p>\n

\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u0644\u062a\u062c\u0627\u0631\u0628 \u0627\u0644\u062a\u064a \u062a\u0645 \u0625\u062c\u0631\u0627\u0624\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 n<\/em> \u060c \u0628\u064a\u0646\u0645\u0627 p<\/em> \u0647\u0648 \u0627\u062d\u062a\u0645\u0627\u0644 \u0646\u062c\u0627\u062d \u0643\u0644 \u062a\u062c\u0631\u0628\u0629. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u064a\u062a\u0645 \u0643\u062a\u0627\u0628\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a \u0627\u0644\u0630\u064a \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n

\n

\"X\\sim\\text{Bin}(n,p)\"<\/p>\n<\/p>\n

\u0644\u0627\u062d\u0638 \u0623\u0646\u0647 \u0641\u064a \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u064a\u062a\u0645 \u062a\u0643\u0631\u0627\u0631 \u0646\u0641\u0633 \u0627\u0644\u062a\u062c\u0631\u0628\u0629 \u0628\u0627\u0644\u0636\u0628\u0637 n<\/em> \u0645\u0631\u0627\u062a \u0648\u062a\u0643\u0648\u0646 \u0627\u0644\u062a\u062c\u0627\u0631\u0628 \u0645\u0633\u062a\u0642\u0644\u0629 \u0639\u0646 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u062d\u062a\u0645\u0627\u0644 \u0646\u062c\u0627\u062d \u0643\u0644 \u062a\u062c\u0631\u0628\u0629 \u0647\u0648 \u0646\u0641\u0633\u0647 (p)<\/em> .<\/p>\n

\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646<\/strong> . <\/p>\n

<\/span> \u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646<\/span><\/h2>\n

\u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0631\u0623\u064a\u0646\u0627 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u0633\u0646\u0631\u0649 \u0639\u062f\u0629 \u0623\u0645\u062b\u0644\u0629 \u0644\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u062a\u0628\u0639 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0644\u0641\u0647\u0645 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644.<\/p>\n

    \n
  1. \u0639\u062f\u062f \u0645\u0631\u0627\u062a \u0638\u0647\u0648\u0631 \u0627\u0644\u0648\u062c\u0647 \u0639\u0646\u062f \u0631\u0645\u064a \u0642\u0637\u0639\u0629 \u0627\u0644\u0646\u0642\u0648\u062f 25 \u0645\u0631\u0629.<\/span><\/li>\n
  2. \u0639\u062f\u062f \u0627\u0644\u062a\u0633\u062f\u064a\u062f\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0646\u0641\u0630\u0647\u0627 \u0644\u0627\u0639\u0628 \u0643\u0631\u0629 \u0627\u0644\u0633\u0644\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0633\u062f\u062f \u0628\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0633\u0644\u0629 60 \u0645\u0631\u0629 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0645\u0648\u0642\u0639.<\/span><\/li>\n
  3. \u0639\u062f\u062f \u0627\u0644\u0645\u0631\u0627\u062a \u0627\u0644\u062a\u064a \u062d\u0635\u0644\u0646\u0627 \u0641\u064a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0631\u0642\u0645 6 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0631\u0645\u064a \u062d\u062c\u0631 \u0627\u0644\u0646\u0631\u062f 30 \u0645\u0631\u0629.<\/span><\/li>\n
  4. \u0639\u062f\u062f \u0627\u0644\u0646\u0627\u062c\u062d\u064a\u0646 \u0641\u064a \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646 \u0645\u0646 \u0623\u0635\u0644 50 \u0637\u0627\u0644\u0628\u0627\u064b.<\/span><\/li>\n
  5. \u0639\u062f\u062f \u0627\u0644\u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0628\u0629 \u0641\u064a \u0639\u064a\u0646\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 100 \u0645\u0646\u062a\u062c.<\/span> <\/li>\n<\/ol>\n

    <\/span> \u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<\/span><\/h2>\n

    \u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a x\u060c n\u060c p\u060c<\/em> \u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0639\u0644\u0649 \u0623\u0646\u0647\u0627 \u0627\u0644\u0631\u0642\u0645 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a \u0644\u0640 n<\/em> \u0641\u064a x<\/em> \u0645\u0631\u0627\u062a p x<\/sup><\/em> \u0645\u0631\u0627\u062a (1-p) nx<\/sup><\/em> .<\/p>\n

    \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u062d\u0633\u0627\u0628 \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646<\/strong> \u0647\u064a: <\/p>\n

    \"\u0635\u064a\u063a\u0629<\/figure>\n

    \ud83d\udc49 \u064a\u0645\u0643\u0646\u0643 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0623\u062f\u0646\u0627\u0647 \u0644\u062d\u0633\u0627\u0628 \u0627\u062d\u062a\u0645\u0627\u0644 \u0648\u062c\u0648\u062f \u0645\u062a\u063a\u064a\u0631 \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646.<\/u><\/p>\n

    \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u062a\u0631\u0627\u0643\u0645\u064a \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062c\u0645\u0639 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a \u0639\u062f\u062f \u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u062c\u0627\u062d \u0627\u0644\u0645\u0639\u0646\u064a\u0629 \u0648\u062c\u0645\u064a\u0639 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629. \u0644\u0630\u0627\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u062a\u0631\u0627\u0643\u0645\u064a \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0647\u064a: <\/p>\n

    \n

    \"\\displaystyle<\/p>\n<\/p>\n

    <\/span> \u062a\u0645\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646<\/span><\/h2>\n
      \n
    • \u0623\u0644\u0642\u064a\u0646\u0627 \u0642\u0637\u0639\u0629 \u0646\u0642\u0648\u062f 10 \u0645\u0631\u0627\u062a\u060c \u0645\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 6 \u0635\u0648\u0631\u061f<\/li>\n<\/ul>\n

      \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0623\u0646 \u062c\u0645\u064a\u0639 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0625\u0637\u0644\u0627\u0642 \u0645\u0633\u062a\u0642\u0644\u0629 \u0639\u0646 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636 \u0648\u0644\u0647\u0627 \u0623\u064a\u0636\u064b\u0627 \u0646\u0641\u0633 \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0646\u062c\u0627\u062d.<\/p>\n

      \u0628\u0634\u0643\u0644 \u0645\u0644\u0645\u0648\u0633\u060c \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0646\u062c\u0627\u062d \u0647\u0648 50\u066a\u060c \u062d\u064a\u062b \u0623\u0646 \u0646\u062a\u064a\u062c\u0629 \u0648\u0627\u062d\u062f\u0629 \u0641\u0642\u0637 \u0645\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u062a\u064a\u0646 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u062a\u064a\u0646 \u062a\u0639\u062a\u0628\u0631 \u0646\u0627\u062c\u062d\u0629.<\/p>\n

      \n

      \"p=\\cfrac{1}{2}=0,5\"<\/p>\n<\/p>\n

      \u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u062a\u0648\u0632\u064a\u0639 \u0647\u0630\u0627 \u0627\u0644\u062a\u0645\u0631\u064a\u0646 \u0647\u0648 \u0630\u0648 \u062d\u062f\u064a\u0646 \u0628\u0625\u062c\u0645\u0627\u0644\u064a 10 \u062a\u062c\u0627\u0631\u0628 \u0648\u0627\u062d\u062a\u0645\u0627\u0644 0.5.<\/p>\n

      \n

      \"X\\sim\\text{Bin}(10<\/p>\n<\/p>\n

      \u0644\u0630\u0627\u060c \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0633\u062a\u0629 \u0635\u0648\u0631\u060c \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646.<\/p>\n

      \n

      \"\\begin{aligned}P[X=x]&=\\begin{pmatrix}n\\\\x\\end{pmatrix}p^x(1-p)^{n-x}\\\\[2ex]P[X=6]&=\\begin{pmatrix}10\\\\6\\end{pmatrix}0,5^6(1-0,5)^{10-6}\\\\[2ex]P[X=6]&=0,2051\\end{aligned}\"<\/p>\n<\/p>\n

      \u0644\u0630\u0627\u060c \u0641\u0625\u0646 \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0633\u062a\u0629 \u0635\u0648\u0631 \u0628\u0627\u0644\u0636\u0628\u0637 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0631\u0645\u064a \u0642\u0637\u0639\u0629 \u0646\u0642\u0648\u062f \u0639\u0634\u0631 \u0645\u0631\u0627\u062a \u0647\u0648 20.51%. <\/p>\n

      <\/span> \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646<\/span><\/h2>\n

      \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n

        \n
      • \u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0645\u0639\u0644\u0645\u062a\u064a\u0646: n<\/em> \u0647\u0648 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u062a\u062c\u0627\u0631\u0628 \u0628\u0631\u0646\u0648\u0644\u064a\u060c \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c p<\/em> \u0647\u0648 \u0627\u062d\u062a\u0645\u0627\u0644 \u0646\u062c\u0627\u062d \u0643\u0644 \u062a\u062c\u0631\u0628\u0629 \u0628\u0631\u0646\u0648\u0644\u064a.<\/li>\n<\/ul>\n

        \n

        \"\\begin{array}{c}X\\sim\\text{Bin}(n,p)\\\\[2ex]n\\geq<\/p>\n<\/p>\n

          \n
        • \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u064a\u0633\u0627\u0648\u064a \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u0644\u062a\u062c\u0627\u0631\u0628 \u0645\u0636\u0631\u0648\u0628\u064b\u0627 \u0641\u064a \u0627\u062d\u062a\u0645\u0627\u0644 \u0646\u062c\u0627\u062d \u0643\u0644 \u062a\u062c\u0631\u0628\u0629. \u0644\u0630\u0644\u0643\u060c \u0644\u062d\u0633\u0627\u0628 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u064a\u062c\u0628 \u0636\u0631\u0628 n<\/em> \u0641\u064a p<\/em> .<\/li>\n<\/ul>\n

          \n

          \"E[X]=n\\cdot<\/p>\n<\/p>\n

            \n
          • \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u064a\u0633\u0627\u0648\u064a \u0625\u062c\u0645\u0627\u0644\u064a \u0639\u062f\u062f \u0627\u0644\u0645\u062d\u0627\u0648\u0644\u0627\u062a \u0645\u0636\u0631\u0648\u0628\u064b\u0627 \u0641\u064a \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0646\u062c\u0627\u062d \u0648\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0641\u0634\u0644.<\/li>\n<\/ul>\n

            \n

            \"Var(X)=n\\cdot<\/p>\n<\/p>\n

              \n
            • \u0635\u064a\u063a\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/li>\n<\/ul>\n

              \n

              \"\\displaystyle<\/p>\n<\/p>\n

                \n
              • \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u062a\u0631\u0627\u0643\u0645\u064a \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0647\u064a:<\/li>\n<\/ul>\n

                \n

                \"\\displaystyle<\/p>\n<\/p>\n

                  \n
                • \u0645\u062c\u0645\u0648\u0639 \u062a\u0648\u0632\u064a\u0639\u064a\u0646 \u0645\u0633\u062a\u0642\u0644\u064a\u0646 \u0630\u0648\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0646\u0641\u0633 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 \u064a\u0639\u0627\u062f\u0644 \u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0646\u0641\u0633 \u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 p<\/em> \u0648 n<\/em> \u0647\u0648 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u0645\u062d\u0627\u0648\u0644\u0627\u062a \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u064a\u0646.<\/li>\n<\/ul>\n

                  \n

                  \"\\begin{array}{c}X\\sim\\text{Bin}(n,p)\\qquad<\/p>\n<\/p>\n

                  \n

                  \"\\displaystyle<\/p>\n<\/p>\n

                    \n
                  • \u062a\u0648\u0632\u064a\u0639 \u0628\u0631\u0646\u0648\u0644\u064a \u0647\u0648 \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u062d\u064a\u062b n=1<\/em> \u060c \u0623\u064a \u064a\u062a\u0645 \u062a\u0646\u0641\u064a\u0630 \u062a\u062c\u0631\u0628\u0629 \u0648\u0627\u062d\u062f\u0629 \u0641\u0642\u0637.<\/li>\n<\/ul>\n

                    \n

                    \"X\\sim\\text{Bin}(1,p)<\/p>\n<\/p>\n

                      \n
                    • \u0625\u0630\u0627 \u0643\u0627\u0646<\/sub> X<\/sub><\/em> 1 ,<\/em> X<\/sub> 2<\/sub> ,\u2026, X k<\/sub><\/em> \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0645\u0633\u062a\u0642\u0644\u0629 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0642\u0628\u064a\u0644 <\/li>\n<\/ul>\n

                      \n

                      \"\\displaystyle\\sum_{i=1}^k<\/p>\n<\/p>\n

                      <\/span> \u062d\u0627\u0633\u0628\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<\/span><\/h2>\n

                      \u0623\u062f\u062e\u0644 \u0642\u064a\u0645 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a p \u0648n<\/em> \u0648 x<\/em> \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644. \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0631\u064a\u062f \u062d\u0633\u0627\u0628\u0647\u0627 \u0648\u0625\u062f\u062e\u0627\u0644 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0642\u0637\u0629 \u0643\u0641\u0627\u0635\u0644 \u0639\u0634\u0631\u064a\u060c \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644 0.1667.<\/p>\n

                      \n
                      \u27a4<\/strong><\/span> \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0646\u062c\u0627\u062d \u0643\u0644 \u062a\u062c\u0631\u0628\u0629 \u2192<\/strong><\/span><\/p>\n

                      \"p<\/p>\n

                      <\/span> <\/div>\n

                      \u27a4<\/strong><\/span> \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u0644\u062a\u062c\u0627\u0631\u0628 \u0627\u0644\u062a\u064a \u062a\u0645 \u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u2192<\/strong><\/span><\/p>\n

                      \"n<\/p>\n

                      <\/span> <\/div>\n

                      \u27a4<\/strong><\/span> \u0639\u062f\u062f \u0627\u0644\u062a\u062c\u0627\u0631\u0628 \u0627\u0644\u0646\u0627\u062c\u062d\u0629: <\/div>\n
                      <\/p>\n

                      \"X=\"<\/p>\n

                      <\/div>\n

                      <\/p>\n

                      \"X\\leq\"<\/p>\n

                      <\/div>\n

                      <\/p>\n

                      \"X\\geq\"<\/p>\n

                      <\/div>\n

                      <\/p>\n

                      \"\\leq<\/p>\n

                      <\/div>\n

                      <\/div>\n<\/form>\n","protected":false},"excerpt":{"rendered":"

                      \u062a\u0634\u0631\u062d \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u0627\u0647\u064a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0627\u062a \u0648\u0641\u064a\u0645 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647. \u0648\u0644\u0630\u0644\u0643 \u0633\u062a\u062c\u062f \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u0648\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0648\u062e\u0635\u0627\u0626\u0635 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u0648\u0641 \u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u062d\u0633\u0627\u0628 \u0623\u064a \u0627\u062d\u062a\u0645\u0627\u0644 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a. \u0645\u0627 \u0647\u0648 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646\u061f \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"\n\u25b7 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u2013 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0648\u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0627\u062a<\/title>\n<meta name=\"description\" content=\"\u062a\u0634\u0631\u062d \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u0627\u0647\u064a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0627\u062a \u0648\u0641\u064a\u0645 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647. \u0644\u0630\u0644\u0643 \u0633\u062a\u062c\u062f \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u2705\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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