# If the following is a probability distribution function: #f(x)=k(e^(-x^2)+e^-x)#, what is #k# and what is the variance?

##### 1 Answer

Mar 31, 2016

There is no such

#### Explanation:

The area under a probability density function is 1.

Therefore,

#int_{-oo}^{oo} f(x) "d"x = 1#

or

#int_{-oo}^{oo} k(e^{-x^2}+e^{-x}) "d"x = 1#

However, the integral

#int_{-oo}^{oo} k(e^{-x^2}+e^{-x}) "d"x #

does not converge for any value of

That is because the integral

#int_{-oo}^{oo} e^{-x} "d"x #

itself is divergent.

Therefore, there is no solution for