Answer to Question #299000 in Statistics and Probability for April

Question

Suppose three coins are toosed let y be the random variables representing the number of heads that occur.

A. Find the values of the random variables Y. Complete the table below.

Answer 1

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

Sample space S is all possible outcomes of three tosses of a coin.

$$S = \{HHH, THH, HTH, HHT,$$

$$TTH, THT, HTT, TTT\}$$

A. Let $y$ be the random variables representing the number of heads that occur. The possible values of $y$ are $0,1,2,3.$

B.

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & y \\ \hline HHH & 3 \\ \hdashline THH & 2 \\ \hdashline HTH &2 \\ \hdashline HHT & 2 \\ \hdashline TTH & 1 \\ \hdashline THT & 1 \\ \hdashline HTT & 1 \\ \hdashline TTT & 0 \\ \hdashline \end{array}$$

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