Math, asked by game6999, 10 months ago

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

Answers

Answered by MaheswariS
0

\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

https://brainly.in/question/16076454

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