Let X and Y have a trinomial distribution with n = 2, pX = 1/4, and pY = 1/2.
(a) Give E(Y | x).
(b) Compare your answer in part (a) with the equation of the line of best fit in Example 4.2-2. Are they the same? Why or why not?
References Example 4.2-2
Step 1 of 5 :
We have that X and Y have the trinomial distribution with n=2, p(X)=and p(Y)=.
The joint probability mass function of x and Y is given as
Step 2 of 5:
We have to find the conditional expectation of Y given X.
That is we have to find E(Y|X=x)
The marginal probability mass function of X is given by
The property of trinomial distribution states that the marginal; distribution of the variables X and Y is Binomial.
Step 3 of 5:
The conditional probability mass function of Y given X=x is given by