Question

已知随机变量ξ只能取-1,0,1,2四个值, 相应概率依次为c,2c,3c,4c, 确定常数c求Eξ,Dξ和η=ξ^2的概率分布

Answer 1

你好！
c+2c+3c+4c=1
解得：c=0.1
所以相应概率依次为0.1,0.2,0.3,0.4
Eξ=-1*0.1+0.3+0.4*2=1
Dξ=(Eξ)^2-Eξ^2=1-0.4=0.6
如果对你有帮助，望采纳。

Answer 2

由归一性
c
+
2c
+
3c
+
4c
=
1
解得：c
=
0.1
Eξ
=
-1c
+
3c
+
2*4c
=
10c
=
1
Eξ^2
=
(-1)^2c
+
3c
+
2^2*4c
=
20c
=
2
Dξ
=
Eξ^2
-
(Eξ)^2
=
2
-
1
=
1
因为ξ只能取-1,0,1,2四个值，所以
η
只能取0,1,4
这三个值。
因此，η=ξ^2的概率分布为
P(η
=
0)
=
P(ξ
=
0)
=
2c
=
0.2
P(η
=
1)
=
P(ξ
=
-1)
+
P(ξ
=
1)
=
c
+
3c
=
4c
=
0.4
P(η
=
4)
=
P(ξ
=
2)
=
4c
=
0.4