Answer to Question #289075 in Statistics and Probability for Nana

Question

Toss a fair coin thrice. Let x denote the number of tails. Find Var(x)

Answer 1

Let us now write out all the possible outcomes from tossing 3 coins in a row:

{HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

Hence n=8

A probability distribution is basically all the possible values of the random variable and their corresponding probabilities. So for our case, this would be the probability distribution:

Variance=$\sum x^2*p(x)-\mu^2$

where $\mu=\sum x*p(x)$

=$(0*\frac{1}{8})+(1*\frac{3}{8})+(2*\frac{3}{8})+(3*\frac{1}{8})$

$=\frac{3}{2}$

Now we will find the sum :

$\sum x^2*p(x)=(0^2*\frac{1}{8})+(1^2*\frac{3}{8})+(2^2*\frac{3}{8})+(3^2*\frac{1}{8})$

$=3$

Hence variance =$\sum x^2*p(x)-\mu^2$

$=3-(\frac{3}{2})^2$

$=\frac{3}{4}$