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## Homework Statement

If X is a discrete random variable having a probability mass function p(x), the expectation or the

expected value of X, denoted E[X], is defined to be

E[X]=Σ x*p(x)

A biased coin is tossed until “heads” appears for the first time. If the probability of a “head” for

the coin is 2

5 , the expected number of tosses needed to get “heads” for the first time is given b

Σ(n*2/5*(3/5)^(n-1)

the summation is from n=1 to infinite.

Compute the expected value. (the expected value need not be an integer.)

## Homework Equations

Σ(n*2/5*(3/5)^(n-1)=5/2

## The Attempt at a Solution

First I found the number of tosses needed to get heads, but I don't understand how to interpret this in the E[X] formula.

I know that my

p(x)=.40

what is my x ? "tails for the first time" ? how to translate it in a numerical representation ?

and the summation is from n=0 to n=2.5 ??

Thanks,

Roni.