Please answer ALL PARTS: a,b,c,d,e,f,g,h, and i . Thank you in advance! Suppose

Question

Please answer ALL PARTS: a,b,c,d,e,f,g,h, and i. Thank you in advance!

Suppose that X and Y are discrete random variables with the following density function f(x, y) f (1, 3) = 0.40, f(1, 6) = 0.20, f(1, 9) = 0.10, f(2, 3) = 0.15, f(2, 6) = 0.08, f(2, 9) = 0.07. (a) Determine the expected value of X. (b) Determine the expected value of Y. (c) Determine the expected value of XY. (d) Determine the marginal density function for X. (e) Determine the marginal density of Y. (f) Given X = 2, find the conditional density function of Y. (g) Determine the variance of Y. (h) Find the probability that X + Y is greater than or equal to 8. (i) Given that Y > 3, find the probability that X = 2.

Explanation / Answer

1)a) E(X) = 1*(0.4+0.2+0.1)+2*(0.15+0.08+0.07) = 1.3

b)E(Y) = 3*(0.4+0.15)+6*(0.2+0.08)+9*(0.10+0.07) = 4.86

c)E(XY) = 0.4*1*3 +0.2*1*6+0.1*1*9 + 0.15*2*3*0.08*2*6+0.07*2*9 = 5.424

d) P(X =1) = 0.4+0.2+0.1 = 0.7

P(X =2) = 0.15+0.08+0.07 = 0.3

Please ask other arts again,you can include this solution when you ask again. Thanks

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