Problem 18.19 Let X be uniformly distributed on the set-3,-1, 1,3). Find E(X2

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

Answer:- Given: X has discrete uniform distribution on set

X={-3,-1,1,3}.

Here X1=-3, X2=-1, X3=1, X4=3 & pmf of X is

p[X=x]=1/4 for all Xi

The expected value of X^2 is ,

E[X^2]= $\sum$ (x^2)*p[X=x]

= (-3^2)*(1/4)+(-1^2)*(1/4)+(1^2)*(1/4)+(3^2)*(1/4)

=(1/4)*{9+1+1+9}

=5

Hence E[X^2]=5

Note: X^2= Square of X

*=Multiplication

E[X^2]=Expected value of X-square

Answer 2

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