{"id":1346,"date":"2023-07-26T19:00:35","date_gmt":"2023-07-26T19:00:35","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%b0%e0%a5%87%e0%a4%b2%e0%a5%87-%e0%a4%b5%e0%a4%bf%e0%a4%a4%e0%a4%b0%e0%a4%a3\/"},"modified":"2023-07-26T19:00:35","modified_gmt":"2023-07-26T19:00:35","slug":"%e0%a4%b0%e0%a5%87%e0%a4%b2%e0%a5%87-%e0%a4%b5%e0%a4%bf%e0%a4%a4%e0%a4%b0%e0%a4%a3","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%b0%e0%a5%87%e0%a4%b2%e0%a5%87-%e0%a4%b5%e0%a4%bf%e0%a4%a4%e0%a4%b0%e0%a4%a3\/","title":{"rendered":"\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u092a\u0930\u093f\u091a\u092f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923<\/strong> \u090f\u0915 \u0938\u0924\u0924 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 <a href=\"https:\/\/statorials.org\/hi\/\u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915-\u091a\u0930\/\" target=\"_blank\" rel=\"noopener\">\u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u091a\u0930 \u0915\u094b<\/a> \u092e\u0949\u0921\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u094b \u0915\u0947\u0935\u0932 \u0936\u0942\u0928\u094d\u092f \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u092f\u093e \u0909\u0938\u0938\u0947 \u0905\u0927\u093f\u0915 \u092e\u093e\u0928 \u0932\u0947 \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0907\u0938\u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0918\u0928\u0924\u094d\u0935 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0939\u0948:<\/span><\/p>\n<p> <span style=\"color: #000000;\">f(x; \u03c3) = (x\/\u03c3 <sup>2<\/sup> )e <sup>-x <sup>2<\/sup> \/(2\u03c3 <sup>2<\/sup> )<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u091c\u0939\u093e\u0902 \u03c3 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0938\u094d\u0915\u0947\u0932 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0941\u0923 \u0939\u0948\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0914\u0938\u0924:<\/strong> \u03c3\u221a <span style=\"border-top: 1px solid black;\">\u03c0\/2<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0935\u093f\u091a\u0932\u0928:<\/strong> ((4-\u03c0)\/2)\u03c3 <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u092e\u094b\u0921:<\/strong> \u03c3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u091a\u0942\u0901\u0915\u093f \u03c0 \u0915\u093e \u090f\u0915 \u091c\u094d\u091e\u093e\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u092e\u093e\u0928 \u0939\u0948, \u0939\u092e \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930 \u0938\u0930\u0932 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0914\u0938\u0924:<\/strong> 1.253\u03c3<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0935\u093f\u091a\u0932\u0928:<\/strong> 0.429\u03c3 <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u092e\u094b\u0921:<\/strong> \u03c3<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0935\u093f\u091c\u093c\u0941\u0905\u0932\u093e\u0907\u091c\u093c\u0947\u0936\u0928<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u094d\u0930\u093e\u092b \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0906\u0915\u093e\u0930 \u0915\u094b \u0926\u093f\u0916\u093e\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u0938\u094d\u0915\u0947\u0932 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u0947 \u0932\u093f\u090f \u0905\u0932\u0917-\u0905\u0932\u0917 \u092e\u093e\u0928 \u0932\u0947\u0924\u093e \u0939\u0948:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13154 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/rayleigh1.png\" alt=\"\u0930\u0947\u0932\u0947 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923\" width=\"419\" height=\"377\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u0938\u094d\u0915\u0947\u0932 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u093e \u092e\u093e\u0928 \u091c\u093f\u0924\u0928\u093e \u092c\u0921\u093c\u093e \u0939\u094b\u0917\u093e, \u0935\u093f\u0924\u0930\u0923 \u0909\u0924\u0928\u093e \u0939\u0940 \u0935\u094d\u092f\u093e\u092a\u0915 \u0939\u094b\u0917\u093e\u0964<\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>\u092c\u094b\u0928\u0938:<\/strong> \u091c\u094b \u0932\u094b\u0917 \u0909\u0924\u094d\u0938\u0941\u0915 \u0939\u0948\u0902, \u0909\u0928\u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u0928\u0947 \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0917\u094d\u0930\u093e\u092b\u093c \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0906\u0930 \u0915\u094b\u0921 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0939\u0948:<\/span><\/em><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load VGAM package\n<\/span><span style=\"color: #008000;\">library<\/span> (VGAM)\n\n<span style=\"color: #008080;\">#create density plots\n<\/span>curve(drayleigh(x, scale = 0.5), from=0, to=10, col='green')\ncurve(drayleigh(x, scale = 1), from=0, to=10, col='red', add=TRUE)\ncurve(drayleigh(x, scale = 2), from=0, to=10, col='blue', add=TRUE)\ncurve(drayleigh(x, scale = 4), from=0, to=10, col='purple', add=TRUE)\n\n<span style=\"color: #008080;\">#add legend\n<\/span>legend(6, 1, legend=c(\"\u03c3=0.5\", \"\u03c3=1\", \"\u03c3=2\", \"\u03c3=4\"),\n       col=c(\"green\", \"red\", \"blue\", \"purple\"), lty=1, cex=1.2)\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u0905\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u092c\u0902\u0927<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0905\u0928\u094d\u092f \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923\u094b\u0902 \u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092c\u0902\u0927 \u0939\u0948:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u091c\u092c \u0938\u094d\u0915\u0947\u0932 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 (\u03c3) <span style=\"color: #000000;\">1 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 2 \u0921\u093f\u0917\u094d\u0930\u0940 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930\u0924\u093e \u0915\u0947 \u0938\u093e\u0925 \u091a\u0940-\u0938\u094d\u0915\u094d\u0935\u093e\u092f\u0930 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0935\u0947\u0907\u092c\u0941\u0932 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u090f\u0915 \u0935\u093f\u0936\u0947\u0937 \u092e\u093e\u092e\u0932\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0906\u0915\u093e\u0930 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 k = 2 \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> \u0938\u094d\u0915\u0947\u0932 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u03c3 \u0915\u0947 \u0938\u093e\u0925 \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u091a\u093e\u0935\u0932 (0, \u03c3) \u0915\u0947 \u0938\u093e\u0925 \u091a\u093e\u0935\u0932 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u092e\u0947\u0902, \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0928\u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0938\u092e\u0941\u0926\u094d\u0930 \u092e\u0947\u0902 \u0932\u0939\u0930\u094b\u0902 \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u094b \u092e\u0949\u0921\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0932\u0939\u0930\u094b\u0902 \u0915\u094b \u0909\u0928\u0915\u0947 \u0936\u093f\u0916\u0930 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a\u0928\u0947 \u092e\u0947\u0902 \u0932\u0917\u0928\u0947 \u0935\u093e\u0932\u093e \u0938\u092e\u092f \u0914\u0930 \u0932\u0939\u0930\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0939\u0941\u0902\u091a\u093e\u0908 \u0917\u0908 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u091a\u0941\u0902\u092c\u0915\u0940\u092f \u0905\u0928\u0941\u0928\u093e\u0926 \u0907\u092e\u0947\u091c\u093f\u0902\u0917 \u092e\u0947\u0902 \u092a\u0943\u0937\u094d\u0920\u092d\u0942\u092e\u093f \u0921\u0947\u091f\u093e \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u094b \u092e\u0949\u0921\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u090f\u092e\u0906\u0930\u0906\u0908 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> \u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092a\u094b\u0937\u0923 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092e\u0947\u0902 \u092e\u0928\u0941\u0937\u094d\u092f\u094b\u0902 \u0914\u0930 \u091c\u093e\u0928\u0935\u0930\u094b\u0902 \u092e\u0947\u0902 \u092a\u094b\u0937\u0915 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0947 \u0938\u094d\u0924\u0930 \u0914\u0930 \u092a\u094b\u0937\u0923 \u0938\u0902\u092c\u0902\u0927\u0940 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u092e\u0949\u0921\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0938\u0902\u0938\u093e\u0927\u0928<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923\u094b\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/hi\/\u0938\u093e\u092e\u093e\u0928\u094d\u092f-\u0935\u093f\u0924\u0930\u0923-1\/\" target=\"_blank\" rel=\"noopener\">\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u092a\u0930\u093f\u091a\u092f<\/a><br \/> <a href=\"https:\/\/statorials.org\/hi\/\u0926\u094d\u0935\u093f\u092a\u0926-\u092c\u0902\u091f\u0928-1\/\" target=\"_blank\" rel=\"noopener\">\u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u092a\u0930\u093f\u091a\u092f<\/a><br \/> <a href=\"https:\/\/statorials.org\/hi\/\u092e\u091b\u0932\u0940-\u0915\u093e-\u0935\u093f\u0924\u0930\u0923\/\" target=\"_blank\" rel=\"noopener\">\u092a\u0949\u0907\u0938\u0928 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e 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\u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0939\u0948: f(x; \u03c3) = (x\/\u03c3 2 )e -x 2 \/(2\u03c3 2 ) \u091c\u0939\u093e\u0902 \u03c3 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0938\u094d\u0915\u0947\u0932 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0939\u0948\u0964 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1346","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0930\u0947\u0932\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u090f\u0915 \u092a\u0930\u093f\u091a\u092f - \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940<\/title>\n<meta name=\"description\" content=\"\u092f\u0939 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