Question

  

Question 1) (60 Marks) a) Given the joint pdf of the continuous RVs X and Y: fxy(x, y) = c for the region {0 sxs y, 0 sy s 1} and zero elsewhere.Where "c" is a constant. Determine if the RV X and Y are independent. (30 Marks) b) Given the following information. For a certain form of illness, (call the illness "A"), the likelihood of having the illness is 0.1 if the person is a smoker and 0.005 if the person is not a smoker. In a doctor's office 20% of the patients are smokers. What is the probability that a randomly selected patient in the office has the illness? (30 Marks)

need urgent, no need to write it neat and clean, just send solutions in 10 to 15 minutes..

b0bGr..

Answer 1

a) The point pdf is O느거느y의 finy) = e . We know that SS fan de daal. xy SO, is e dy dx = 1 gl dn=1 or, selym dn = 1 on s c(1-x) dx = 1 2 ۵۲) C or, e [1 - 1 2 or, c=2 OLAL Y EI finy) = 2 f(x) s fca, y) dy as 2 [y] X 2(1-x) Y Y f(x) = s feat) dx = /2 dx = 2 (x7) = 24 f(x) f(y) = 2(1-x) + 2Y = 4 (1-x) y ... f(x,y) f(a) fly) X and y, are not independent So,

6 Let de fine events and s represent illness and Smokep Here given values are P(11) - 0.1 P(IIS) = 0.005 -P(S)=20% = 0.20 P (SC) = 1-PCS) = -0.20 = 0.80 we need to find the probability randomly selected person has illness, lie, PLi) using to fol Probability, P (I) = P(S) P(ILS) + PCS) P(115) = 0.20 xool to.80 x 0.005 - 0.024 The probability of illness is 0.024