1. ## E[Y] and V[Y]

Given random variable X with following probability mass function:

2. ## Re: E[Y] and V[Y]

really?

$E[Y] = \sum y p[y] = \sum 2^x p[x]$

$E[Y^2] = \sum y^2 p[y] = \sum 2^{2x} p[x]$

$V[Y] = E[Y^2] - (E[Y])^2$

I leave you to do the number crunching

3. ## Re: E[Y] and V[Y]

hi, thanks, i follow those formula,
E[Y]=2 x 0.3 + 4 x0.5 + 8 x 0.2 = 4.2
E[Y^2] = 4 x 0.3 + 16 x0.5 + 64x 0.2 = 22
V[Y]= 22-4.2=17.8

how i can calculate a, b?

4. ## Re: E[Y] and V[Y]

Originally Posted by Amanda2018
hi, thanks, i follow those formula,
E[Y]=2 x 0.3 + 4 x0.5 + 8 x 0.2 = 4.2
E[Y^2] = 4 x 0.3 + 16 x0.5 + 64x 0.2 = 22
V[Y]= 22-4.2=17.8

how i can calculate a, b?
You made a mistake in the last line. You forgot to square E[Y]. It should be

$$V[Y]=22-4.2^2=4.36$$

For $a,b$ you have $E[Z]=aE[x]+b=0$ and $V[Z]=E[Z^2]-(E[Z])^2=\sum (ax+b)^2p[x]=1$