consider-the-following-pdf-of-a-random-variable-X-f-x-i-0-x-2-i-i-0-otherwise-x-gt-0-find-the-variance-X-

Question Number 148620 by jlewis last updated on 29/Jul/21

consider the following pdf of

a random variable X

f (x) = {\sum_{i = 0}^{\infty} {[(- x^{2}) i / i!]}_{0 otherwise}^{x > 0}

find the variance X

Answered by Olaf_Thorendsen last updated on 29/Jul/21

f (x) = \underset{i = 0}{\sum^{\infty}} {(- 1)}^{i} \frac{x^{2 i}}{i!} = e^{- x^{2}}

\int_{x > 0} f (x) d x = \int_{0}^{+ \infty} e^{- x^{2}} d x = \frac{\sqrt{π}}{2} \neq 1

This is not a pdf .