Question

•Box A and B contains 1, 2, 3, 4. Construct the probability distribution and draw a histogram of the sum when one number from each box is  taken with placement

Answer 1

Let $X$ be a random variable represented by the sum of the outcomes, There are $4^2=16$ possible outcomes with replacement

$2: (1, 1)$

$3: (1, 2), (2, 1)$

$4: (1, 3), (2, 2), (3, 1)$

$5: (1, 4), (2, 3), (3, 2), (4, 1)$

$6: (2, 4), (3,3),(4, 2)$

$7: (3,4), (4, 3)$

$8: (4,4)$

Construct the probability distribution

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline p(x) & 1/16 & 1/8 & 3/16 & 1/4 & 3/16 & 1/8 & 1/16 \end{array}$$

Draw a histogram