Question

Suppose that X follows an exponential distribution

?(?) = {??

-?? 0,, | ? ? > ≤ 0 0 |

And let’s assume random variable ? = 2? + 4 find the expected value of Y. (?[?])

Answer #1

Solution :

Given that, X follows an exponential distribution with parameter ?.

The probability density function of X is given by,

The expected value of X would be as follows :

Integrating by parts we get,

We have, Y = 2X + 4

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