Chapter 15.7, Problem 12P

Let $x=$ number of heads in one toss of a coin. What are the possible values of $x$ and their probabilities? What is ${\mu }_x?$ Hence show that $=\frac{1}{4},$ so the standard deviation is $\frac{1}{2}.$ Now use the result from Problem 6.15 "variance of a sum of independent random variables = sum of their variances" to show that if $x=$ number of heads in $n$ tosses of a coin, and the standard deviation ${\sigma }_x=\frac{1}{2}\sqrt{n}$.