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kap26 [50]
4 years ago
6

Suppose that 3 balls are randomly selected from an urn containing 3 red, 4 white, and 5 blue balls. Let X and Y denote, respecti

vely, 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).]

Mathematics
2 answers:
arlik [135]4 years ago
4 0

Answer:

<em>Let X  and Y be our given values</em>

Step-by-step explanation:

<em>For further explanation kindly find the attached step by step approach</em>

Mkey [24]4 years ago
3 0

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.

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