The probability distribution of a discrete random variable $X$ is given by \(P(X=x)=\frac{x^2}{14}

Question

The probability distribution of a discrete random variable $X$ is given by $P(X=x)=\frac{x^2}{14}$, $x\in\{1,2,k\}$, where $k>0$. Write down $P(X = 2)$.[1] Show that $k = 3$. [4] Find $E(X)$.[2]

Accepted Answer

$E(X)=\frac{1(1)+2(4)+3(9)}{14}=\frac{18}{7}$.

Determine an unknown discrete probability distribution and its expectation.

Determine an unknown discrete probability distribution and its expectation.

Solution:

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