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.

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I need solution of part b and c only
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.
Transcribed Image Text: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.
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