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1. Refer to Exercise 23. Assume that the probabilities that each of the three scenarios occurs are P(A) = 0.20, P(B) = 0.30, and P(C) = 0.50.
a. Find the probability that scenario A occurs and that the loss is 5%.
b. Find the probability that the loss is 5%.
c. Find the probability that scenario A occurs given that the loss is 5%.
2. A box contains four 75 W lightbulbs, three 60 W lightbulbs, and three burned-out lightbulbs. Two bulbs are selected at random from the box. Let X represent the number of 75 W bulbs selected, and let Y represent the number of 60 W bulbs selected.
a. Find the joint probability mass function of X and Y.
b. Find µX .
c. Find µY .
d. Find σX .
e. Find σY .
f. Find Cov(X,Y).
g. Find ρX,Y .
3. A fair coin is tossed five times. Which sequence is more likely, HTTHH or HHHHH? Or are they equally likely? Explain.
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