Explore BrainMass

# Random Variables

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Let X1,X2... be a sequence of independent and identically distributed continuous random variables. Define the random variable ...
(a) Compute the p.m.f of N by first computing P(N [less than or equal to] n)
(b) Show that E(N)=e

*(Please see attachement for complete problem)

https://brainmass.com/statistics/probability/continuous-random-variables-independent-factors-28958

#### Solution Preview

First, we need to find the probability that . Since are independent and identically distributed continuous random variables, by symmetry, we know that
and . So,

Secondly, we know ...

#### Solution Summary

Let X1,X2... be a sequence of independent and identically distributed continuous random variables. Define the random variable ...
(a) Compute the p.m.f of N by first computing P(N [less than or equal to] n)
(b) Show that E(N)=e

\$2.49