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Question

Statistics Question on Multivariate Distributions

Let 𝑋 be a random variable such that the moment generating function of 𝑋 exists in a neighborhood of zero and
E(Xn)=(−1)n25+2n+15+15,E(X^n)=(-1)^n\frac{2}{5}+\frac{2^{n+1}}{5}+\frac{1}{5}, n=1,2,3,…..
Then, 𝑃 (|𝑋-12\frac{1}{2}|>1) equals

A

15\frac{1}{5}

B

25\frac{2}{5}

C

35\frac{3}{5}

D

45\frac{4}{5}

Answer

45\frac{4}{5}

Explanation

Solution

The correct option is (D): 45\frac{4}{5}