Question

The probability distribution function of a random variable is given by f(x) = 2-x, 1<x<2. Find E(X^2)
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Answer 1

SOLUTION

GIVEN

The probability distribution function of a random variable is given by f(x) = 2-x, 1 < x < 2

TO DETERMINE

$\: E({X}^{2} )$

EVALUATION

$\: E({X}^{2} )$

$= \displaystyle \int\limits_{1}^{2} (2 - x) \, dx$

$= \displaystyle (2x - \frac{ {x}^{2} }{2} ){\bigg|}_{1}^{2}$

$= \displaystyle (4 - 2) - \bigg(2 - \frac{1}{2} \bigg)$

$= \displaystyle \bigg(2 - \frac{3}{2} \bigg)$

$= \displaystyle \frac{1}{2}$

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