Question

Question 1(a&b)
Question 3 (a,b,c,d)

QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x, x.) = 0, otherwise. (4 marks) b) Find F(0.7,0.5). (5 marks) c) Find the marginal probability density function for X, and X2 (6 marks) d) Find the conditional probability density function for X\ given X2 and the conditional probability density function for X2 given X, (4 marks)

Answer 1

1)

a)

2t_3

2r-3

as f(x,y) = f(x) f(y)

X and Y are independent

b)

X > Y

hence x varies from y to infinity

y vary from 0 to infinity

P(X > Y) =

6e23drdy (Decimal: 0.6) 0

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