Suppose

Y

is a random variable.

Y=0

with probability

0.6,Y=1

. with probability 0.2 , and

Y=2

with probability 0.2 .\ a. What is the mean of

Y

? [ 2 points]\

M=\\\\sum_x Pr[x

]

=

[

x]x=0.6(0)+0.2(1)+0.2(2)=0.6

\ b. What is the variance of

Y

? [2 points]\

\\\\sigma ^(2)=\\\\sum_x Pr[x

]

=

[

x](x-\\\\mu )^(2)=0.6(0-0.6)^(2)+0.2(1-0.6)^(2)+0.2(2-0.6)\ =0.6(0.36)+0.2(0.16)+0.2(1.96)=0.216+0.032+0.392\ \\\\sigma ^(2)=0.64

\ c. What is the standard deviation of

Y

? [1 points]\

\\\\sigma =\\\\sqrt(\\\\sigma ^(2))=\\\\sqrt(0.64)=0.8

Suppose Y is a random variable. Y=0 with probability 0.6,Y=1 with probability 0.2 , and Y=2 with probability 0.2 . a. What is the mean of Y ? [2 points] =xPr[X=x]x=0.6(0)+0.2(1)+0.2(2)=0.6 b. What is the variance of Y ? [2 points] 22=xPr[X=x](x)2=0.6(00.6)2+0.2(10.6)2+0.2(20.=0.6(0.36)+0.2(0.16)+0.2(1.96)=0.216+0.032+0.392=0.64 c. What is the standard deviation of Y ? [1 points] =2=0.64=0.8