STAT_333_Assignment_2 - STAT 333 Assignment 2 Due Thursday...

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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 6-sided die is rolled repeatedly. Let λ be the event “the maximum roll so far is ≤ 5” a. Explain carefully why λ is a renewal event. b. Determine the renewal sequence { r n } c. Find f λ by any legitimate method. Is λ recurrent or transient? d. Find the expected number of occurrences of λ. 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 26-letter 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 6-sided die 4. A fair 6-sided die is rolled repeatedly. Consider the event “333”, which is delayed renewal. A fair 6-sided die is rolled repeatedly....
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This note was uploaded on 12/12/2010 for the course STAT 333 taught by Professor Chisholm during the Spring '08 term at Waterloo.

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