STAT 333 mid2review

# STAT 333 mid2review - Midterm 2 Review 1(Stat 333 Winter...

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Midterm 2 Review 1. (Stat 333 Winter 2010) Suppose a monkey randomly and independently hits the white notes on a piano repeatedly, one at a time. The notes are { A,B,C,D,E,F,G } . (a) Find the expected number of trials until the monkey ﬁrst plays the melody ”C D C D E D C D C”. (b) (Additional Part) Using the delayed renewal theorem, ﬁnd the expected number of trials until the monkey ﬁrst plays the melody ”C C D C C A C C D C C”. (For practice, ﬁnd the p.g.f. F λ ( z ) of the ﬁrst occurrence of this event and show that F 0 λ (0) gives the same result.) (c) Derive the p.g.f, F CDC ( z ) of the waiting time until the monkey ﬁrst plays ”C D C”. (d) Find the probability that ”C D C” occurs for the ﬁrst time on trial 6. (e) What two things are required for a delayed renewal event to occur inﬁnitely often? (f) (Additional Part) Derive the p.m.f. of T CC , the waiting time until ”CC” ﬁrst occurs. 2. (Stat 333 Winter 2010) Consider a Markov Chain with state space

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STAT 333 mid2review - Midterm 2 Review 1(Stat 333 Winter...

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