Let X1 X2 and X3 be three random variables that take on valu

Let X1, X2 and X3 be three random variables that take on values plusminus 1 with probabilities 1/2. Define X = (X1 + X2 + X3)/3 to be the sample average of the three random variables. What values can X take on? Carefully define both the pmf and cdf for X and graph both.

Solution

a) x bar being average of x1, x2, x3 can take values as -1,-1/3, 1/3, and 1

Pdf is given below

b)

x bar	-1	-0.33333	-0.33333	1
p	0.125	0.375	0.375	0.125	1
Cum prob	0.125	0.5	0.875	1