# Random Variables

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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)

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:06 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/continuous-random-variables-independent-factors-28958

#### Solution Preview

See attachment please!

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