Consider four multi-valued random variables C (campus), G (grade), M (major), and Y (year). We know that none of these variables are independent. We are provided the probability tables for the following joint, marginal, and conditional probabilities. P(Y) P(M) P(G,Y) P(C|Y) P(C,M) P(Y|M) For example, we are told: P(M=compSci) = 0.3, P(M=psych) = 0.2, P(M=bio)=0.2, P(M=business)=0.1P(G=A,Y=freshman)=0.03, P(G=B,Y=freshman)=0.12 , ... P(G=F , Y=senior)=0.08[corrected Jan 18, 11am] We are not provided any other probability tables; for example, we are not given values for: P(G=B) or P(M=psych, Y=junior) Explain how to combine probabilities from above to compute each probability below, or write“not possible” if it is not possible. For example: P(Y) = ∑? ?(?, ? = ?)
a) P(Y=freshman | C =RH)
Consider four multi-valued random variables C (campus), G (grade), M (major), and Y (year). We know...
Consider four multi-valued random variables C (campus), G (grade), M (major), and Y (year). We know that none of these variables are independent. We are provided the probability tables for the following joint, marginal, and conditional probabilities. P(Y) P(M) P(G,Y) P(C|Y) P(C,M) P(Y|M) For example, we are told: P(M=compSci) = 0.3, P(M=psych) = 0.2, P(M=bio)=0.2, P(M=business)=0.1P(G=A,Y=freshman)=0.03, P(G=B,Y=freshman)=0.12 , ... P(G=F , Y=senior)=0.08[corrected Jan 18, 11am] We are not provided any other probability tables; for example, we are not given values...
and Y ~ Geometric - 4 Let X ~ Geometric We assume that the random variables X and Y are statistically independent. Answer the following questions: a (3 marks) For all x E 10,1,2,...^, show that 2+1 P(X>x) P(x (3 = Similarly, for all y [0,1,2,...^, show that Show your working only for one of the two identities that are pre- sented above. Hint: You may use the following identity without proving it. For any non-negative integer (, we have:...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...