{"id":3935,"date":"2023-07-14T16:10:59","date_gmt":"2023-07-14T16:10:59","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%99%e1%80%bb%e1%80%be%e1%80%b1%e1%80%ac%e1%80%ba%e1%80%99%e1%80%be%e1%80%94%e1%80%ba%e1%80%b8%e1%80%90%e1%80%94%e1%80%ba%e1%80%96%e1%80%ad%e1%80%af%e1%80%b8-x2\/"},"modified":"2023-07-14T16:10:59","modified_gmt":"2023-07-14T16:10:59","slug":"%e1%80%99%e1%80%bb%e1%80%be%e1%80%b1%e1%80%ac%e1%80%ba%e1%80%99%e1%80%be%e1%80%94%e1%80%ba%e1%80%b8%e1%80%90%e1%80%94%e1%80%ba%e1%80%96%e1%80%ad%e1%80%af%e1%80%b8-x2","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%99%e1%80%bb%e1%80%be%e1%80%b1%e1%80%ac%e1%80%ba%e1%80%99%e1%80%be%e1%80%94%e1%80%ba%e1%80%b8%e1%80%90%e1%80%94%e1%80%ba%e1%80%96%e1%80%ad%e1%80%af%e1%80%b8-x2\/","title":{"rendered":"X^2 \u104f \u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/\u1000\u103b\u1015\u1014\u103a\u1038-\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1000\u103b\u1015\u1014\u103a\u1038 \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/a> X \u1000\u102d\u102f \u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u101e\u100a\u1037\u103a \u1021\u1010\u103d\u1000\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a X <sup>2<\/sup> \u104f \u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>E(X <sup>2<\/sup> ) = \u03a3x <sup>2<\/sup> * p(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u2211<\/strong> : \u201c\u1015\u1031\u102b\u1004\u103a\u1038\u201d \u101f\u1030\u101e\u1031\u102c \u101e\u1004\u103a\u1039\u1000\u1031\u1010\u104a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : \u1000\u103b\u1015\u1014\u103a\u1038 variable \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p(x)<\/strong> : \u1000\u103b\u1015\u1014\u103a\u1038 variable \u101e\u100a\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u101a\u1030\u101e\u100a\u1037\u103a\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u101e\u100a\u103a \u1024\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1021\u101e\u102f\u1036\u1038\u1001\u103b\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- X <sup>2<\/sup> \u104f \u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u104b<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u1015\u1014\u103a\u1038 variable \u1010\u1005\u103a\u1001\u102f\u104f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u1031\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1007\u101a\u102c\u1038\u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-31621 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/x2_1.jpg\" alt=\"\" width=\"266\" height=\"253\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">X <sup>2<\/sup> \u104f \u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = \u03a3x <sup>2<\/sup> * p(x)<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = (0) <sup>2<\/sup> *.06 + (1) <sup>2<\/sup> *.15 + (2) <sup>2<\/sup> *.17 + (3) <sup>2<\/sup> *.24 + (4) <sup>2<\/sup> *.23 + (5) <sup>2<\/sup> *.\u1040\u1049 + (\u1046) <sup>\u1042<\/sup> *.\u1040\u1046<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = 0 + 0.15 + 0.68 + 2.16 + 3.68 + 2.25+ 2.16<\/span><\/p>\n<p> <span style=\"color: #000000;\">E( <sup>X2<\/sup> ) = 11.08<\/span><\/p>\n<p> <span style=\"color: #000000;\">X <sup>2<\/sup> \u104f\u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103e\u102c <strong>11.08<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1000\u103b\u1015\u1014\u103a\u1038 variable \u101e\u100a\u103a <strong>discrete random variable<\/strong> \u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1000\u1014\u1037\u103a\u1021\u101e\u1010\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u101e\u102c \u101a\u1030\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">X \u101e\u100a\u103a <strong>\u1005\u1009\u103a\u1006\u1000\u103a\u1019\u1015\u103c\u1010\u103a \u1000\u103b\u1015\u1014\u103a\u1038\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1019\u103e\u102f<\/strong> \u1016\u103c\u1005\u103a\u1015\u102b\u1000\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a X <sup>2<\/sup> \u104f\u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = \u222b x <sup>2<\/sup> f(x)dx<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u222b- \u201c\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u100a\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u201d \u101f\u1030\u101e\u1031\u102c \u101e\u1004\u103a\u1039\u1000\u1031\u1010\u104a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>f(x)<\/strong> : <a href=\"https:\/\/statorials.org\/my\/cdf-\u1014\u103e\u1004\u1037\u103a-pdf\/\" target=\"_blank\" rel=\"noopener\">pdf \u101e\u100a\u103a<\/a> \u1000\u103b\u1015\u1014\u103a\u1038 variable \u1021\u1010\u103d\u1000\u103a \u1006\u1000\u103a\u101c\u1000\u103a\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1005\u1009\u103a\u1006\u1000\u103a\u1019\u1015\u103c\u1010\u103a \u1000\u103b\u1015\u1014\u103a\u1038\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c <sup>X2<\/sup> \u104f\u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1024\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1010\u102d\u102f\u1004\u103a\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1015\u102d\u102f\u104d\u1001\u1000\u103a\u1001\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1006\u1031\u102c\u1037\u1016\u103a\u101d\u1032\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u1018\u102f\u1036\u1021\u101c\u102f\u1015\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031-\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f-\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\/\" target=\"_blank\" rel=\"noopener\">\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101b\u103e\u102c\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f-\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101b\u103e\u102c\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f-\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u104f\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101b\u103e\u102c\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1000\u103b\u1015\u1014\u103a\u1038 \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a X \u1000\u102d\u102f \u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u101e\u100a\u1037\u103a \u1021\u1010\u103d\u1000\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a X 2 \u104f \u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b E(X 2 ) = \u03a3x 2 * p(x) \u101b\u103d\u103e\u1031- \u2211 : \u201c\u1015\u1031\u102b\u1004\u103a\u1038\u201d \u101f\u1030\u101e\u1031\u102c \u101e\u1004\u103a\u1039\u1000\u1031\u1010\u104a x : \u1000\u103b\u1015\u1014\u103a\u1038 variable \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038 p(x) : \u1000\u103b\u1015\u1014\u103a\u1038 variable 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