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2. If X and Y are two random variables, having joint density function 1 -(6-x-y) 0≤x≤ 2, 0≤ y ≤ 4 24 f(x, y) = Find a. P(X < 1,Y <3) b. P(X+Y<3) c. P(X < 1|Y <3) 0, otherwise

2. If X and Y are two random variables, having joint density function 1 -(6-x-y) 0≤x≤ 2, 0≤ y ≤ 4 24 f(x, y) = Find a. P(X < 1,Y <3) b. P(X+Y<3) c. P(X < 1|Y <3) 0, otherwise

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.CR: Chapter 13 Review
Problem 42CR
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2. If X and Y are two random variables, having joint density function 1 (6-x-y) 0≤x≤ 2, 0≤ y ≤ 4 24 f(x, y) = 0, otherwise Find a. P(X < 1,Y <3) P(X+Y <3) b. c. P(X < 1|Y < 3) d. P < X < 1<Y <3) (√²/ G e. The conditional distribution of the random variable X for a given Y=y and Y for a given X=X
Transcribed Image Text:2. If X and Y are two random variables, having joint density function 1 (6-x-y) 0≤x≤ 2, 0≤ y ≤ 4 24 f(x, y) = 0, otherwise Find a. P(X < 1,Y <3) P(X+Y <3) b. c. P(X < 1|Y < 3) d. P < X < 1<Y <3) (√²/ G e. The conditional distribution of the random variable X for a given Y=y and Y for a given X=X
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1. Suppose that X is a continuous random variable whose probability density function is given by f(x) = {a(x+3) if2 ≤ x ≤8 otherwise a. What is the value of a? b. Find P{3 < X <5} c. Find the CDF of X d. Find P{X2 4}
Transcribed Image Text:1. Suppose that X is a continuous random variable whose probability density function is given by f(x) = {a(x+3) if2 ≤ x ≤8 otherwise a. What is the value of a? b. Find P{3 < X <5} c. Find the CDF of X d. Find P{X2 4}
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