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Statistics Question on Standard Univariate Distributions

Let XX be a random variable having the Poisson distribution with mean 11. Let g:N∪0→Rg: \mathbb{N} \cup \\{0\\} \to \mathbb{R} be defined by
g(x)={1if x∈0,2 0if x∉0,2g(x) = \begin{cases} 1 & \text{if } x \in \\{0, 2\\} \\\ 0 & \text{if } x \notin \\{0, 2\\} \end{cases}
Then E(g(X))E(g(X)) is equal to:

A

e−1e^{-1}

B

2e−12e^{-1}

C

52e−1\frac{5}{2} e^{-1}

D

32e−1\frac{3}{2} e^{-1}

Answer

32e−1\frac{3}{2} e^{-1}

Explanation

Solution

The correct option is (D): 32e−1\frac{3}{2} e^{-1}