Question

Question 1) (60 Marks) a) Given the joint pdf of the continuous RVs X and Y: ???(?, ?) = ? ??? ?ℎ? ?????? {0 ≤ ? ≤ ?, 0 ≤ ? ≤ 1} ??? ???? ?????ℎ???.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

Answer 1

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b) of having illness is Given that likelihood y the person is smoker. P (Ils) = od S-smoker PC II 3) = 0.005 Not smoker. ie Illness 207 of patients are smokers. AME Whe so PCS) 20 we have to find PCI) PCI IS) = PC Ins) PIS) - 0 PCIOS) = 0.1 X 0.2 ㅋ P(1) - polos) P (3) PCF15) - Plîos) P(3) 0.005 EP (f) - 0.02 80/100 P (I) P (I) -0.02 = (0.005) X0.8) 0.024 ㅕ