(a) Find E[R]. Express your answer in terms of p and/or n. (b) (Extra Practice. Not Graded.) Find var (R). Express your answer in terms of p and/or n.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider a sequence of independent tosses of a biased coin at times k = 0, 1, 2, ..., n. On
each toss, the probability of Heads is p, and the probability of Tails is 1 - p.
A reward of one unit is given at time k, for k € {1, 2,..., n}, if the toss at time k resulted
in Tails and the toss at time k - 1 resulted in Heads. Otherwise, no reward is given at
time k.
Let R be the sum of the rewards collected at times 1, 2,..., n.
(a) Find E[R]. Express your answer in terms of p and/or n.
(b) (Extra Practice. Not Graded.) Find var (R). Express your answer in terms of p
and/or n.
Transcribed Image Text:Consider a sequence of independent tosses of a biased coin at times k = 0, 1, 2, ..., n. On each toss, the probability of Heads is p, and the probability of Tails is 1 - p. A reward of one unit is given at time k, for k € {1, 2,..., n}, if the toss at time k resulted in Tails and the toss at time k - 1 resulted in Heads. Otherwise, no reward is given at time k. Let R be the sum of the rewards collected at times 1, 2,..., n. (a) Find E[R]. Express your answer in terms of p and/or n. (b) (Extra Practice. Not Graded.) Find var (R). Express your answer in terms of p and/or n.
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