1. Consider a container which has a large number of coins and suppose that each of the coins has some probability of turning up heads when it is tossed. However, this probability varies from coin to coin. Suppose that the composition of the container is such that if a coin is chosen at random from the container, then its heads probability can be regarded as being the value of a rv X that is Beta distributed with parameters m e Z+ and n e Z+. Suppose that a coin is selected at random from the container and tossed k e Z+ times. Out of these k tosses, let Y denote the number of heads obtained. (a) Find the marginal pmf of Y. (b) Determine Var(Y). (c) Determine the conditional distribution of X|(Y = y), as well as its associated mean and variance.
1. Consider a container which has a large number of coins and suppose that each of the coins has some probability of turning up heads when it is tossed. However, this probability varies from coin to coin. Suppose that the composition of the container is such that if a coin is chosen at random from the container, then its heads probability can be regarded as being the value of a rv X that is Beta distributed with parameters m e Z+ and n e Z+. Suppose that a coin is selected at random from the container and tossed k e Z+ times. Out of these k tosses, let Y denote the number of heads obtained. (a) Find the marginal pmf of Y. (b) Determine Var(Y). (c) Determine the conditional distribution of X|(Y = y), as well as its associated mean and variance.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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