Question

Let function f(x) = (9/13) (1/3)x , x = 0, 1, 2 be the probability mass function of a discrete random variable X. Then the Mean of X is

Answer 1

$\textbf{Given:}$

$\text{Probability mass function is f(x)=(\dfrac{9}{13})(\dfrac{1}{3})^x }$

$\textbf{To find:}$

$\text{Mean of X}$

$\textbf{Solution:}$

$\text{Mean of X is given by}$

$\bf\,E(X)=\Sigma\;{x\,f(x)}$

$\implies\,E(X)=(0)\,f(0)+(1)\,f(1)+(2)\,f(2)$

$\implies\,E(X)=(0)(\dfrac{9}{13})(\dfrac{1}{3})^0+(1)(\dfrac{9}{13})(\dfrac{1}{3})^1+(2)(\dfrac{9}{13})(\dfrac{1}{3})^2$

$\implies\,E(X)=0+(1)(\dfrac{9}{13})(\dfrac{1}{3})+(2)(\dfrac{9}{13})(\dfrac{1}{9})$

$\implies\,E(X)=(\dfrac{9}{13})(\dfrac{1}{3})[1+\dfrac{2}{3}]$

$\implies\,E(X)=(\dfrac{9}{13})(\dfrac{1}{3}})(\dfrac{5}{3})$

$\implies\,E(X)=(\dfrac{3}{13})(\dfrac{5}{3})$

$\implies\bf\,E(X)=\dfrac{5}{13}$

$\therefore\textbf{The mean of X is \bf\,\dfrac{5}{13} }$

Find more:

Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(X ≤ 2) = k/(2)¹⁶, then k is equal to :

(A) 17 (B) 137 (C) 1 (D) 121

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