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At time 0, a coin that comes up heads with probability p
Chapter 4, Problem 70P(choose chapter or problem)
Problem 70P
At time 0, a coin that comes up heads with probability p is flipped and falls to the ground. Suppose it lands on heads. At times chosen according to a Poisson process with rate λ, the coin is picked up and flipped. (Between these times, the coin remains on the ground.) What is the probability that the coin is on its head side at time t?
Questions & Answers
QUESTION:
Problem 70P
At time 0, a coin that comes up heads with probability p is flipped and falls to the ground. Suppose it lands on heads. At times chosen according to a Poisson process with rate λ, the coin is picked up and flipped. (Between these times, the coin remains on the ground.) What is the probability that the coin is on its head side at time t?
ANSWER:
Solution :
Step 1 of 1:
From the given information a coin that comes up heads with probability p is flipped and
Then a Poisson process with mean rate .
Our goal is:
We need to find the probability that the coin is on its head side of time t.