\\(a , b , c\\) \u306f\u7570\u306a\u308b \\(3\\) \u3064\u306e\u6b63\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\u6b21\u306e\u30c7\u30fc\u30bf\u306f \\(2\\) \u3064\u306e\u79d1\u76ee X \u3068 Y \u306e\u8a66\u9a13\u3092\u53d7\u3051\u305f \\(10\\) \u4eba\u306e\u5f97\u70b9\u3092\u307e\u3068\u3081\u305f\u3082\u306e\u3067\u3042\u308b.\r\n\\[\r\n\\begin{array}{c|cccccccccc} & [1] & [2] & [3] & [4] & [5] & [6] & [7] & [8] & [9] & [10] \\\\ \\hline \\text{\u79d1\u76ee X \u306e\u5f97\u70b9} & a & c & a & b & b & a & c & c & b & c \\\\ \\hline \\text{\u79d1\u76ee Y \u306e\u5f97\u70b9} & a & b & b & b & a & a & b & a & b & a \\end{array}\r\n\\]\r\n\u79d1\u76ee X \u306e\u5f97\u70b9\u306e\u5e73\u5747\u5024\u3068\u79d1\u76ee Y \u306e\u5f97\u70b9\u306e\u5e73\u5747\u5024\u3068\u306f\u7b49\u3057\u3044\u3068\u3059\u308b.<\/p>\r\n
(1)<\/strong>\u3000\u79d1\u76ee X \u306e\u5f97\u70b9\u306e\u5206\u6563\u3092 \\({s _ X}^2\\) , \u79d1\u76ee Y \u306e\u5f97\u70b9\u306e\u5206\u6563\u3092 \\({s _ Y}^2\\) \u3068\u3059\u308b. \\(\\dfrac{{s _ X}^2}{{s _ Y}^2}\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n (2)<\/strong>\u3000\u79d1\u76ee X \u306e\u5f97\u70b9\u3068\u79d1\u76ee Y \u306e\u5f97\u70b9\u306e\u76f8\u95a2\u4fc2\u6570\u3092, \u56db\u6368\u4e94\u5165\u3057\u3066\u5c0f\u6570\u7b2c \\(1\\) \u4f4d\u307e\u3067\u6c42\u3081\u3088.<\/p><\/li>\r\n (3)<\/strong>\u3000\u79d1\u76ee X \u306e\u5f97\u70b9\u306e\u4e2d\u592e\u5024\u304c \\(65\\) , \u79d1\u76ee Y \u306e\u5f97\u70b9\u306e\u6a19\u6e96\u504f\u5dee\u304c \\(11\\) \u3067\u3042\u308b\u3068\u304d, \\(a , b , c\\) \u306e\u7d44\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \u79d1\u76ee X , Y \u305d\u308c\u305e\u308c\u306e\u5e73\u5747\u5024 \\(E (X) , E (Y)\\) \u306f\r\n\\[\r\nE(X) = \\dfrac{3a+3b+4c}{10} , \\quad E(Y) = \\dfrac{5a+5b}{10}\r\n\\]\r\n\u6761\u4ef6\u3088\u308a \\(E(X) = E(Y)\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n3a+3b+4c & = 5a+5b \\\\\r\n\\text{\u2234} \\quad c & = \\dfrac{a+b}{2} \\quad ... [1]\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nE(X) = E(Y) = c = \\dfrac{a+b}{2}\r\n\\]\r\n\u3053\u308c\u3089\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n{s _ X}^2 & = E \\left( X^2 \\right) -\\left\\{ E(X) \\right\\}^2 \\\\\r\n& = \\dfrac{1}{10} \\left( 3a^2 +3b^2 +4c^2 \\right) -\\left( \\dfrac{a+b}{2} \\right)^2 \\\\\r\n& = \\dfrac{1}{5} \\left( 2a^2 +ab +2b^2 \\right) -\\dfrac{1}{4} \\left( a^2 +2ab +b^2 \\right) \\\\\r\n& = \\dfrac{1}{20} \\left( 3a^2 -6ab +3b^2 \\right) \\\\\r\n& = \\dfrac{3}{20} (a-b)^2\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\\begin{align}\r\n{s _ Y}^2 & = E \\left( Y^2 \\right) -\\left\\{ E(Y) \\right\\}^2 \\\\\r\n& = \\dfrac{1}{10} \\left( 5a^2 +5b^2 \\right) -\\left( \\dfrac{a+b}{2} \\right)^2 \\\\\r\n& = \\dfrac{1}{2} \\left( a^2 +b^2 \\right) -\\dfrac{1}{4} \\left( a^2 +2ab +b^2 \\right) \\\\\r\n& = \\dfrac{1}{4} \\left( a^2 -2ab +b^2 \\right) \\\\\r\n& = \\dfrac{1}{4} (a-b)^2\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\dfrac{{s _ X}^2}{{s _ Y}^2} = \\dfrac{\\dfrac{3}{20}}{\\dfrac{1}{4}} = \\underline{\\dfrac{3}{5}}\r\n\\]\r\n (2)<\/strong><\/p>\r\n \u79d1\u76ee X, Y \u306e\u5f97\u70b9\u306e\u5171\u5206\u6563\u3092 \\(s _ {XY}\\) \u3068\u304a\u304f. (3)<\/strong><\/p>\r\n[1] \u3088\u308a, \\(c\\) \u306f \\(a\\) \u3068 \\(b\\) \u306e\u5e73\u5747\u5024\u3067\u3042\u308a, \u79d1\u76ee X \u306e\u5f97\u70b9 \\(a , b , c\\) \u306e\u983b\u5ea6\u306f\u305d\u308c\u305e\u308c \\(3 , 3 , 4\\) \u3060\u304b\u3089, \u79d1\u76ee X \u306e\u5f97\u70b9\u306e\u4e2d\u592e\u5024\u306f\r\n\\[\r\n\\dfrac{c+c}{2} = c = 65\r\n\\]\r\n\u307e\u305f\r\n\\[\\begin{align}\r\nc = \\dfrac{a+b}{2} & = 65 \\\\\r\n\\text{\u2234} \\quad a+b & = 130 \\quad ... [3]\r\n\\end{align}\\]\r\n\u79d1\u76ee Y \u306e\u6a19\u6e96\u504f\u5dee\u304c \\(11\\) \u306a\u306e\u3067, [2] \u3088\u308a\r\n\\[\\begin{align}\r\ns _ Y = \\dfrac{1}{2} |a-b| & = 11 \\\\\r\n\\text{\u2234} \\quad |a-b| & = 22 \\quad ... [4]\r\n\\end{align}\\]\r\n[3] [4] \u3088\u308a\r\n\\[\r\n( a , b ) = ( 76 , 54 ) , ( 54 , 76 )\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n( a , b , c ) = \\underline{( 76 , 54 , 65 ) , ( 54 , 76 , 65 )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a , b , c\\) \u306f\u7570\u306a\u308b \\(3\\) \u3064\u306e\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \u6b21\u306e\u30c7\u30fc\u30bf\u306f \\(2\\) \u3064\u306e\u79d1\u76ee X \u3068 Y \u306e\u8a66\u9a13\u3092\u53d7\u3051\u305f \\(10\\) \u4eba\u306e\u5f97\u70b9\u3092\u307e\u3068\u3081\u305f\u3082\u306e\u3067\u3042\u308b. \\[ \\begin{array}{c| … \u7d9a\u304d\u3092\u8aad\u3080
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n
\r\n[1] \u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\ns _ {XY} & = \\dfrac{1}{10} \\left( 4 \\cdot \\dfrac{a-b}{2} \\cdot \\dfrac{a-b}{2} +2 \\cdot \\dfrac{a-b}{2} \\cdot \\dfrac{b-2}{2} +4 \\cdot 0 \\right) \\\\\r\n& = \\dfrac{1}{20} (a-b)^2\r\n\\end{align}\\]\r\n(1)<\/strong> \u306e\u904e\u7a0b\u3088\u308a, \u79d1\u76ee X, Y \u306e\u5f97\u70b9\u306e\u6a19\u6e96\u504f\u5dee \\(s _ X , s _ Y\\) \u306f\u305d\u308c\u305e\u308c\r\n\\[\\begin{align}\r\ns _ X & = \\sqrt{{s _ X}^2} = \\dfrac{\\sqrt{15}}{10} |a-b| \\\\\r\ns _ Y & = \\sqrt{{s _ Y}^2} = \\dfrac{1}{2} |a-b| \\quad ... [2]\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u76f8\u95a2\u4fc2\u6570 \\(r\\) \u306f\r\n\\[\r\nr = \\dfrac{s _ {XY}}{s _ {X} s _ {Y}} = \\dfrac{\\dfrac{1}{20}}{\\dfrac{\\sqrt{15}}{10} \\cdot \\dfrac{1}{2}} = \\dfrac{\\sqrt{15}}{15}\r\n\\]\r\n\u3053\u3053\u3067 \\(3.8 \\lt \\sqrt{15} \\lt 3.9\\) \u306a\u306e\u3067, \u8fba\u3005\u3092 \\(15\\) \u3067\u5272\u308b\u3068\r\n\\[\r\n0.25 \\cdots \\lt \\dfrac{\\sqrt{15}}{15} \\lt 2.6\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5024\u306f\r\n\\[\r\n\\underline{0.3}\r\n\\]\r\n