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Unformatted text preview: STAT 333 Assignment 2 Due: Thursday, June 24 at the beginning of class 1. Prove the Delayed Renewal Relation. (Hint: the proof is very similar to that of the Renewal Relation, and you have to be very careful with the starting values of sums.) 2. A fair 6sided die is rolled repeatedly. Let be the event the maximum roll so far is 5 a. Explain carefully why is a renewal event. b. Determine the renewal sequence { r n } c. Find f by any legitimate method. Is recurrent or transient? d. Find the expected number of occurrences of . e. Repeat c and d for the similar event the maximum roll so far is 3. Comment on the differences in the values. 3. Use the Renewal Theorem to find the average time until the first occurrence of: a. ABRACADABRA in random draws from the 26letter alphabet b. H T H H T in tosses of a coin with P(H) = p c. 1 2 1 2 1 4 1 2 1 2 1 in rolls of a fair 6sided die 4. A fair 6sided die is rolled repeatedly. Consider the event 333, which is delayed renewal. A fair 6sided die is rolled repeatedly....
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 Spring '08
 Chisholm

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