Question

5.Consider a discrete random variable X with the probability mass function xp(x) Consider Y-g(X) 0.2 0.4 0.3 0.1 a)Find the probability distribution of Y b) Find the expected value of Y, E(Y) Does μ Y equal to g(μx)? 4

Answer 1

from above below is probability distribution of Y:

x	y=1/x	P(y)
4	1/4	0.10
3	1/3	0.30
2	1/2	0.40
1	1	0.20

b) E(Y) =$\mu$_Y =$\sum$yP(y) =(1/4)*0.1+(1/3)*0.3+(1/2)*0.4+1*(0.2)=0.525

as  $\mu$_x =$\sum$xP(x) =1*0.2+2*0.4+3*0.3+4*0.1=2.3

therefore g( $\mu$_x)=1/2.3 =0.4348 which is not equal to $\mu$_Y