If X is a random variable such that E(X^2) = E(X) = 1, then what is E(X^100) ?

Options are as follows:
A) 1
B) 2^100
C) 0
D) None of the above

The answer to this question in an answer key was found to be A), but I have no idea about how to proceed to solve this. A detailed explanation would help a lot.

1 Answer
May 8, 2018

"See explanation"

Explanation:

"Since"
"variance = "E(X^2) - (E(X))^2
"which is here : "1 - 1^2 = 0,"
"there is no variance."
"This means that all values of X are equal to the mean E(X) = 1."
"So X is always 1."
"Hence "X^100 = 1.
=> E[X^100] = 1