2.33. Suppose that the random variables X and Y have a joint density function given by fx, y) = {c(2x + y) 2 2), (e) P(X >3), (f) P(X + Y >4), (g) the joint distribution func- tion, (h) whether X and Y are independent. (a) The total probability is given by

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2.33. Suppose that the random variables X and Y have a joint density function given by
ſc(2x + y) 2 < x< 6, 0 < y < 5
f(x, y) = {
otherwise
Find (a) the constant c, (b) the marginal distribution functions for X and Y, (c) the marginal density func-
tions for X and Y, (d) P(3 <X< 4, Y > 2), (e) P(X > 3), (f) P(X + Y > 4), (g) the joint distribution func-
tion, (h) whether X and Y are independent.
(a) The total probability is given by
Transcribed Image Text:2.33. Suppose that the random variables X and Y have a joint density function given by ſc(2x + y) 2 < x< 6, 0 < y < 5 f(x, y) = { otherwise Find (a) the constant c, (b) the marginal distribution functions for X and Y, (c) the marginal density func- tions for X and Y, (d) P(3 <X< 4, Y > 2), (e) P(X > 3), (f) P(X + Y > 4), (g) the joint distribution func- tion, (h) whether X and Y are independent. (a) The total probability is given by
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