I have this random variable X. I know that P(X=c)=1 for some real number c. I want to calculate EX2, but I have no idea how to do this. I know that EX=c and I tried to do it with integrating:
∫ccx2dx, but this is just 0. So how should I do this?
Answer
Since {X=c}⊆{X2=c2} we have that
1=P(X=c)≤P(X2=c2)≤1
and hence also P(X2=c2)=1. Can you calculate the expectation now?
Another approach is to note that Var(X)=E[(X−c)2]=0 but on the other hand we have the formula
Var(X)=E[X2]−E[X]2,
which enables us to calculate E[X2].
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