Your pocket contains a random number N of coins, where N follows the Poisson distribution with parameter d. All the coins are identical and weighted so that the probability of landing on head is p. Call X the random variable giving the number of heads obtained after tossing all the coins. Show that X is distributed as a Poisson random variable with parameter Xp.
Your pocket contains a random number N of coins, where N follows the Poisson distribution with parameter d. All the coins are identical and weighted so that the probability of landing on head is p. Call X the random variable giving the number of heads obtained after tossing all the coins. Show that X is distributed as a Poisson random variable with parameter Xp.
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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Transcribed Image Text:2. Your pocket contains a random number N of coins, where N follows the Poisson
distribution with parameter A. All the coins are identical and weighted so that the
probability of landing on head is p. Call X the random variable giving the number
of heads obtained after tossing all the coins. Show that X is distributed as a Poisson
random variable with parameter Xp.
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