The probability density function of the random variable X is given by f ( x )=1/40 for 20 < x < 60 , and zero elsewhere

Economics Nov 07, 2020

The probability density function of the random variable X is given by f ( x )=1/40 for 20 < x < 60 , and zero elsewhere . The expected value , E ( X ) , of the random variable X is :

Select one :

a.5

b.28

c.15

d.30

e.None of the answers is correct

Expert Solution

Expected value = $\sum$ x * f(x)

Expected value = 1 * 0 + 2 * 0 + 3 * 0 + ...... + 20 * 0 + 21 * (1 / 40) + 22 * (1 / 40) + .......... + 59 * (1 / 40) + 60 * 0 + 61 * 0 ..........

Expected value = 21 * (1 / 40) + 22 * (1 / 40) + .......... + 59 * (1 / 40) = [(21 + 22 + 23 + 24 + ........ + 59) / 40] = (1,560 / 40) = 39

Option E is correct.

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