从一批含有13只正品,2只次品的产品中,不放回地抽取3次,每次抽取1只,设抽得次品数为X,则E(5X+1)=______.-数学

题目简介

从一批含有13只正品,2只次品的产品中,不放回地抽取3次,每次抽取1只,设抽得次品数为X,则E(5X+1)=______.-数学

题目详情

从一批含有13只正品,2只次品的产品中,不放回地抽取3次,每次抽取1只,设抽得次品数为X,则E(5X+1)=______.
题型:填空题难度:中档来源:不详

答案

由题意,X的取值为0,1,2,则
P(X=0)=class="stub"13
15
×class="stub"12
14
×class="stub"11
13
=class="stub"22
35
;P(X=1)=class="stub"2
15
×class="stub"13
14
×class="stub"12
13
+class="stub"13
15
×class="stub"2
14
×class="stub"12
13
+class="stub"13
15
×class="stub"12
14
×class="stub"2
13
=class="stub"12
35

P(X=2)=class="stub"13
15
×class="stub"2
14
×class="stub"1
13
+class="stub"2
15
×class="stub"13
14
×class="stub"1
13
+class="stub"2
15
×class="stub"1
14
×class="stub"13
13
=class="stub"1
35

所以期望E(X)=0×class="stub"22
35
+1×class="stub"12
35
+2×class="stub"1
35
=class="stub"14
35

所以E(5X+1)=class="stub"14
35
×5+1
=3
故答案为3.

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