Subject. Probability & statistics Please answer as soon as possible. Thanks Numb

Question

Subject. Probability & statistics Please answer as soon as possible. Thanks Number......6 1. Suppose that a point (X,Y) is chosen randomly from the square S containing all points (x.y) so that 1 T,y S3. Determine he expected value of (x+y) 2. In a drug trial a patient is selected randomly from a number of patients in the study and we record Y, an indicator of the treatment group for the patient and X, indicator of whether or not the patient improved, relapsed or didn't change the state of health. The table presented gives the joint p.f. of X,Y. Compute the marginal distribution of f(X) for X-1, 2, 3 and fW) for Y = 1, 2, 3, 4,5 Resp(X)Group (YTDrug(1) Drug(2)|Drug (3)!Drug(4)Trug(5) Improve (1) Relapse (2) 0.091 0.087 0.043 0.028 0.047 0.101 0.074 | 0.092-0531-0.128-1-0.065 0.056 0.041 | 0.033 | 0.061 Tab. 1: Response X w.r.t Treatment group Y 3. Determine if X and Y are independent in table presented for question 2 4. Find the proper constant value so the following p.d.f that works for the axioms of probability Compute P(3/8

Explanation / Answer

6)
M ~N(73, (5/2)^2)
W ~ N(69 , (5/4)^2)

P( M - W < 0)
M -W ~ N(73 - 69 , (5/2)^2 + (5/4)^2)
~ N(4, 7.8125)
P(M -W < 0)
=P(Z <(0 - 4)/sqrt(7.8125))
= P(Z < -1.431083)
= 0.076200

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