Question

Suppose the random variables X, Y, and Z have the following joint probability distribution. x y z f ( x , y , z ) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 Determine the conditional probability distribution of X given that Y

Answer 1

Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).

answer:

Given that Y = 1 : 2/5

Given that Z = 2 : 3/5

Explanation:

The conditional probability distribution of X F x | yz^( x )

Given that Y = 1

F x | yz . ( x | yz ) = 2/5

Given that z = 2

= 3/5

attached below is the detailed solution