Question

There are three possible values of the random variable Y representing the number of tails. These are 0, 1, and 2. Assign probability values P(Z) to each value of the random variable

Answer 1

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

There are $2^2=4$ possible outcomes

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

The possible values of the random variable $Y$ are $0, 1, 2.$

$$\def\arraystretch{1.5} \begin{array}{c:c} Possible \ Outcomes & Y \\ \hline HH & 0 \\ \hdashline HT & 1 \\ \hdashline TH & 1 \\ \hdashline TT & 2 \\ \end{array}$$

We will assume that the probability of getting heads and tails is the same:

$$p = q =1/2$$

Construct the probability distribution of the random variable

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

or

$$\def\arraystretch{1.5} \begin{array}{c:c} y & 0 & 1 & 2 \\ \hline p(y) & 0.25 & 0.5 & 0.25 \end{array}$$