Question

A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.

Answer 1

Let X = number of heads in 5 tosses. Then the binomial distribution for X has n =5, $p=\frac{1}{2}\text{and}q\mathit{}=\frac{1}{2}$
$$\begin{gathered} P(X=r)={}^{5}C_r{\left(\frac{1}{2}\right)}^r{\left(\frac{1}{2}\right)}^{5-r},r\mathit{}=0,1,2,3,4,5 \\ =\frac{{}^{5}C_r}{2^5} \\ \mathrm{Substituting}r\mathit{}=0,1,2,3,4,5\mathrm{we}\mathrm{get}\mathrm{the}\text{following}\mathrm{probability}\mathrm{disrtribution}. \\ X\mathit{}012345 \\ P\left(X\right)\frac{1}{32}\frac{5}{32}\frac{10}{32}\frac{10}{32}\frac{5}{32}\frac{1}{32} \end{gathered}$$