A-random-variable-K-has-a-pdf-f-k-0-otherwise-e-k-0-gt-k-find-E-K-and-the-cdf-

Question Number 148864 by jlewis last updated on 31/Jul/21

A random variable K has a pdf

f (k) = {_{0, otherwise}^{e^{- k, 0 > k}} find E (K) and

the cdf

Answered by Olaf_Thorendsen last updated on 01/Aug/21

I suppose f (k) = e^{- k} if k > 0 otherwise

f is not a pdf .

\int_{- \infty}^{+ \infty} f (x) d x = \int_{0}^{+ \infty} e^{- x} d x = 1

E (K) = \int_{0}^{+ \infty} {x e}^{- x} d x = {[x (- e^{- x})]}_{0}^{+ \infty}

- \int_{0}^{+ \infty} (- e^{- x}) d x = 1

E (K) = 1

F (k) = \int_{0}^{k} e^{- x} d x = 1 - e^{- k}

F (k) = {\begin{cases} 0 if k < 0 \\ 1 - e^{- k} if k ⩾ 0 \end{cases}

Commented by jlewis last updated on 01/Aug/21

hello sir, from {[x (- e^{- x})]}_{0}^{+ \infty} I dont get

where x has gone, and is x a variable ?

Commented by Olaf_Thorendsen last updated on 01/Aug/21

I noted the variable x, but you can

write instead of x : z, flower, Mickey or

Donald Trump sir, if you prefer .