Question

Two coins are tossed and the random variable Z gives the number of heads. Find the range space, possible outcomes, and give the table of values.

Answer 1

Let's denote H - heads, T - tails.

Sample space S is all possible outcomes.

$$S = \{HH, TH, HT, TT\}$$

A. Let $z$ be the random variables representing the number of heads that occur. The possible values of $z$ are $0,1,2.$

B.

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & y \\ \hline HH & 2 \\ \hdashline TH & 1 \\ \hdashline HT & 1 \\ \hdashline TT & 0 \\ \hdashline \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} z & 0 & 1 & 2 \\ \hline p(z) & 1/4 & 1/2 & 1/4 \end{array}$$