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1. Let Xi = the outcome of the ith roll of a die.
a. What are the expected value and variance of Xi?b. Let Y = the sum of the outcomes of 3 die rolls. What is Yin terms of X,?c. Use the expected value and variance of Xi you found in a. to find the expected value and variance of Y.d. What has to be true in order to sum variances to find the variance of a sum? Is that true in this case? Explain.e. Let W = three times the outcome of the ith roll of the die. What is W in terms of X?f. What are the expected value and variance of W?
2. Describe a situation relevant to your discipline in which you would be interested in the expected value of a mean or sum of random variables. Clearly describe the random variables and the meaning of the mean or sum of them.
3. A coin is tossed 20 times and the number of heads is counted. Let X = the number of heads. What is the distribution of X? Explain.
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