设随机变量X的分布律为P{X=k}=k/15,k=1,2,3,4,5,试求:(1)P{1/2<X<5/2}; (2)P{1<=X<=3}; (3)P{X>3}. 设随机变量X的概率分布为P(X=k)=k/15,k=1,2,...

\u8bbe\u968f\u673a\u53d8\u91cfX\u7684\u6982\u7387\u5206\u5e03\u4e3aP{X=K}=ak(K=1,2,3,4,5),\u786e\u5b9a\u5e38\u6570a

\u4f60\u597d\uff01\u6240\u6709\u6982\u7387\u4e4b\u548c\u4e00\u5b9a\u662f1\uff0c\u5373a+2a+3a+4a+5a=1\uff0c\u6240\u4ee5a=1/15\u3002\u7ecf\u6d4e\u6570\u5b66\u56e2\u961f\u5e2e\u4f60\u89e3\u7b54\uff0c\u8bf7\u53ca\u65f6\u91c7\u7eb3\u3002\u8c22\u8c22\uff01

P(1/2<x<5/2)=P(x=1)+P(x=2)=1/15+2/15=1/5
P(1\u2264x\u22642)=P(x=1)+P(x=2)=1/15+2/15=1/5
\u4f8b\u5982\uff1a
P{1/2<X<5/2}=1/15+2/15=1/5,(x=1\u6216\u80052)
P{1<=X<=3}; =1/15+2/15+3/15=2/5
(3)P{X>3}.=3/5\uff08x=4\u30025\uff09
\u6269\u5c55\u8d44\u6599\uff1a
\u6982\u7387\u5206\u5e03\uff1a\u4e8b\u4ef6\u7684\u6982\u7387\u8868\u793a\u4e86\u4e00\u6b21\u8bd5\u9a8c\u4e2d\u67d0\u4e00\u4e2a\u7ed3\u679c\u53d1\u751f\u7684\u53ef\u80fd\u6027\u5927\u5c0f\u3002\u82e5\u8981\u5168\u9762\u4e86\u89e3\u8bd5\u9a8c\uff0c\u5219\u5fc5\u987b\u77e5\u9053\u8bd5\u9a8c\u7684\u5168\u90e8\u53ef\u80fd\u7ed3\u679c\u53ca\u5404\u79cd\u53ef\u80fd\u7ed3\u679c\u53d1\u751f\u7684\u6982\u7387\uff0c\u5373\u968f\u673a\u8bd5\u9a8c\u7684\u6982\u7387\u5206\u5e03\u3002
\u5982\u679c\u8bd5\u9a8c\u7ed3\u679c\u7528\u53d8\u91cfX\u7684\u53d6\u503c\u6765\u8868\u793a\uff0c\u5219\u968f\u673a\u8bd5\u9a8c\u7684\u6982\u7387\u5206\u5e03\u5c31\u662f\u968f\u673a\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\uff0c\u5373\u968f\u673a\u53d8\u91cf\u7684\u53ef\u80fd\u53d6\u503c\u53ca\u53d6\u5f97\u5bf9\u5e94\u503c\u7684\u6982\u7387\u3002\u6839\u636e\u968f\u673a\u53d8\u91cf\u6240\u5c5e\u7c7b\u578b\u7684\u4e0d\u540c\uff0c\u6982\u7387\u5206\u5e03\u53d6\u4e0d\u540c\u7684\u8868\u73b0\u5f62\u5f0f\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u6982\u7387\u5206\u5e03

P{1/2<X<5/2}=1/15+2/15=1/5,(x=1或者2)
P{1<=X<=3}; =1/15+2/15+3/15=2/5
(3)P{X>3}.=3/5(x=4。5)

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