What are the expected value and variance of xilet y the

Question

1. Let X_i = the outcome of the ith roll of a die.

a. What are the expected value and variance of X_i?
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 X_i 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.