2. If X and Y are two random variables, having joint density function1(6-x-y) 0≤x≤ 2, 0≤ y ≤ 424f(x, y) =0,otherwiseFinda. P(X < 1,Y <3)P(X+Y <3)b.c. P(X < 1|Y < 3)d. P < X < 1

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Answered: 2. If X and Y are two random variables,…

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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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Follow-up Questions

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Follow-up Question

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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