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