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1. (a) W = log (1). Here log is log base e. i. Find the range of W. ii. Find the density of W. The joint distribution of two random variable X and Y is (b) Part (a) and (b) of this question are independent. Suppose a random variable U follows Uniform(0,1) distribution. Define fxy(x, y) = 8 xy 1(0

1. (a) W = log (1). Here log is log base e. i. Find the range of W. ii. Find the density of W. The joint distribution of two random variable X and Y is (b) Part (a) and (b) of this question are independent. Suppose a random variable U follows Uniform(0,1) distribution. Define fxy(x, y) = 8 xy 1(0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.1: Continuous Probability Models
Problem 16E
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1. (a) W = log (). Here log is log base e. i. Find the range of W. ii. Find the density of W. The joint distribution of two random variable X and Y is fxy(x, y) = 8 xy 1(0<y<x<1). Here 8x y1 (0<y<r<1) means 8xy when 0 < y < x < 1 and zero otherwise. Define Z = (b) i. ii. iii. iv. Part (a) and (b) of this question are independent. Suppose a random variable U follows Uniform(0,1) distribution. Define V. X. Find the range of X. Find the range of Z. Find the joint density gx,z(x, z) of X and Z. Hint: Use the change of variable formula for (X, Y) to (X, Z(X,Y)) in Lec. 31. Find the marginal density of X. Find the marginal density of Z. Are X and Z independent?
Transcribed Image Text:1. (a) W = log (). Here log is log base e. i. Find the range of W. ii. Find the density of W. The joint distribution of two random variable X and Y is fxy(x, y) = 8 xy 1(0<y<x<1). Here 8x y1 (0<y<r<1) means 8xy when 0 < y < x < 1 and zero otherwise. Define Z = (b) i. ii. iii. iv. Part (a) and (b) of this question are independent. Suppose a random variable U follows Uniform(0,1) distribution. Define V. X. Find the range of X. Find the range of Z. Find the joint density gx,z(x, z) of X and Z. Hint: Use the change of variable formula for (X, Y) to (X, Z(X,Y)) in Lec. 31. Find the marginal density of X. Find the marginal density of Z. Are X and Z independent?
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