Answer to Question #305377 in Statistics and Probability for MayMay

Question

Three balls of different colors are numbered 1, 2, and 3, Construct a

sampling distribution with n=2. Make a histograrn for this sample

distribution.

Answer 1

Let's denote 1 - ball 1, 2 - ball 2, and 3-ball 3.

Sample space S is all possible outcomes.

$$S = \{12, 13, 21, 23, 31, 32\}$$

Let $Y$ be the random variables representing the sum of numbers of balls that occur. The possible values of $Y$ are $3,4,5.$

$$\def\arraystretch{1.5} \begin{array}{c:c} Possible\ outcomes & Y \\ \hline 12 & 3 \\ \hdashline 13 & 4 \\ \hdashline 21 & 3 \\ \hdashline 23 & 5 \\ \hdashline 31 & 4 \\ \hdashline 32 & 5 \\ \hdashline \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} y & 3 & 4 & 5 \\ \hline p(y) & 1/3 & 1/3 & 1/3 \\ \end{array}$$