Question

Suppose that 3 balls are randomly selected from an urn containing 3 red, 4 white, and 5 blue balls. Let X and Y denote, respectively, the number of red and white balls chosen. (a) Find the distribution of (X, Y ), i.e. find the joint probability mass function of X and Y . (b) Are X and Y independent? [Hint: To show that X and Y are not independent, it is sufficient to find a single pair of numbers x and y such that P(X = x, Y = y) 6= P(X = x, Y = y).]

Answer 1

Answer:

Let X  and Y be our given values

Step-by-step explanation:

For further explanation kindly find the attached step by step approach

Answer 2

Answer:

The joint distributions are shown in the explanation below:

Step-by-step explanation:

Let the set be red balls = 3

                    white balls = 4

                      blue balls = 5

Then the joint distribution is given by the following:

P(0,0) = $\frac{10}{220}$

P(0,1)   = $\frac{40}{220}$

P(0,2) = $\frac{30}{220}$

P(0,3) = $\frac{4}{220}$

P(1,0) = $\frac{30}{220}$

P (1,1) = $\frac{60}{220}$

P (1, 2) = $\frac{18}{220}$

P(2,0) = $\frac{15}{220}$

P (2,1) = $\frac{12}{220}$

P (3,0) = $\frac{1}{220}$

the distributions are then displayed as marginal probability mass functions.