设ξ是离散型随机变量,P(ξ=a)=23,P(ξ=b)=13,且a<b,又Eξ=43,Dξ=29,则a+b的值为______.-数学

题目简介

设ξ是离散型随机变量,P(ξ=a)=23,P(ξ=b)=13,且a<b,又Eξ=43,Dξ=29,则a+b的值为______.-数学

题目详情

设ξ是离散型随机变量,P(ξ=a)=
2
3
,P(ξ=b)=
1
3
,且a<b,又Eξ=
4
3
,Dξ=
2
9
,则a+b的值为______.
题型:填空题难度:中档来源:不详

答案

Eξ=class="stub"4
3
,Dξ=class="stub"2
9
P(ξ=a)=class="stub"2
3
,P(ξ=b)=class="stub"1
3

class="stub"2
3
a+class="stub"1
3
b=class="stub"4
3
(a-class="stub"4
3
)
2
×class="stub"2
3
+(b-class="stub"4
3
)
2
×class="stub"1
3
=class="stub"2
9

∴a=1,b=2则 a+b=3
故答案为:3.

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