Answer to Question #292291 in Statistics and Probability for Yaku

Question

1. An urn contains 4 balls numbered 1, 2, 3, 4, respectively. Let Y be the

number that occurs if one ball is drawn at random from the urn. What is

the probability function for Y ?

2. Consider the urn in Exercise 1. Two balls are drawn the urn without

replacement. Let W be the sum of the two numbers that occur. Find the

probability function for W. Compute μW and \sigma W.

3. Assume the sampling in Exercise 2 is done with replacement and define

random variable W in the same way. Find the probability function for W

and compute its mean and standard deviation.

4. An urn contains five balls numbered 1 to 5. Two balls are drawn simultaneously.

a) Let X be the larger of the two numbers drawn. Find the probability

mass function for random variable X.

b) Let V be the sum of the two numbers drawn. Find the probability

mass function for random variable V .

c) For the random variables in a) and b), find μX, \sigma X, μV and \sigma V .