Exam1Sample

# Exam1Sample - Random Sampling of Questions 1 The...

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Random Sampling of Questions 1. The probability that rain is followed by rain is 0 . 8, a sunny day is followed by rain is 0 . 6. Find the probability that one has two rainy days then two sunny days. 2. Let: f ( x ) = k | x - 2 | , for x = - 1 , 0 , 1 , 3 Find k so that f is a PDF. Find the expected value of X . Find the expected value of X 2 . 3. A balanced die is tossed twice. Let A be the event that an even number comes up on the first toss. Let B be the event that an even number comes up on the second. Let C be the event that the first two tosses gave the same number. Are A, B, C pairwise independent independent? 4. State Bayes’ Theorem. 5. If A, B are independent prove that A and B are independent. 6. What is the difference between saying that A, B, C are independent events, versus saying that X, Y, Z are independent random variables? 7. In a poker game, 5 cards are dealt from a deck of 52. What is the proba- bility of getting a four-of-a-kind?

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