Question

Three coins are tossed and the random variable Z gives the number of tails. Find

the range space, possible outcomes, and give the table of values.

Answer 1

The sample space of a fair coin flip is $\{H, T\}.$ The sample space of a sequence of three fair coin flips is all $2^3=8$ possible sequences of outcomes:

$$\{ HHH, HHT, HT H, HT T,$$

$$T HH, T HT, T T H, T T T\}$$

The possible values for the random variable Z are $0,1,2,3.$

$$\def\arraystretch{1.5} \begin{array}{c:c} z & 0 & 1 & 2 & 3 \\ \hline p(z) & 1/8 & 3/8 & 3/8 & 1/8\\ \end{array}$$