Question

1) An urn contains 10 balls, 2 red, 5 blue, and 3 green balls. Take out 3 balls at a random, without replacement. You win $2 for each green ball you select and lose $3 for each red ball you select. Let the random variable X denote the amount you win, determine the probability mass function of X.

2) Each of the 60 students in a class belongs to exactly one of the three groups A,B, or C. The membership numbers for the 3 groups are as follows:

A: 15 students

B: 20 C: 25 First, Next,

a. b. c.

students
students
choose one of the 60 students at random and let X be the size of that student’s group;.

choose one of the 3 groups at random and let Y be its size. Write down the pmf for X and Y.
Compute ?(?) ??? ?(?).
Compute ???(?) ??? ???(?).

3. Roll a fair die repeatedly. Let X denote the number of 4’s in the first 6 rolls and let Y denote the number of rolls needed to obtain a 2.

a. WritedowntheprobabilitymassfunctionofX. b. WritedowntheprobabilitymassfunctionofY. c. Find an expression for ?(? ≥ 3).
d. Find an expression for ?(? > 6).

Answer 1

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