Question

Box A and Box B both contain the numbers 1, 2, 3 and 4. Construct the probability mass function and draw the histogram of the sum when one number from each box is taken at a time, with replacement.

Answer 1

Let X be a random variable representing the sum of the numbers, then X = {2,3,4,5,6,7,8}

$P(X=2)={\frac 1 {16}}$

$P(X=3)={\frac 2 {16}}={\frac 1 8}$

$P(X=4)={\frac 3 {16}}$

$P(X=5)={\frac 4 {16}}={\frac 1 4}$

$P(X=6)={\frac 3 {16}}$

$P(X=7)={\frac 2 {16}}={\frac 1 8}$

$P(X=8)={\frac 1 {16}}$