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
MattyMatty
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#

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