Please provide name of distribution and variables, show all steps and explain values in words.

A congressional committee is composed of 10 members: 6 Republicans and 4 Democrats. On any given vote, members vote independently. Whereas Republicans always vote their party line, Democrats vote their party line with probability .8, and vote Republican with probability .2. On a rainy day only 3 committee members (selected wfo replacement) were present. Let X = number of Democrats present Y = Number who voted Democratic that day 3. Find the marginal pdf ofX, i.e., P[X=k] for k=0, 1, 2, 3. Display E[X] and VAR[X]. b. Determine the conditional probability that P[ Y=j | X=k] for k=3 and j=0,1,2,3 c. Display the table of joint probabilities M111) for 0 5 j 5 i, i=0,l,2,3 (1. Display the marginal pdf of Y. Is it recognizable? Compute EfY]and VAR[Y]. e. Determine the conditional expectation of Y given that X31, for x=0, 1,2,3. f. Compute the COV(X,Y), possibly using part e. g. Finally compute the CORRELATION (X,Y)