Q2: Find F,(y) and fy(y) if y = -4x+3 and f(x) = 2e-²xU(x).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Q1:
The random variable x is N (5, 2) and y = 2x+4. Find ny, oy, and fy(y).
Q2:
Find F, (y) and fy(y) if y = -4x+3 and fx(x) = 2e-²xU(x).
Q3:
The random variable x is uniform in the interval (0, 1). Find the density of the random
variable y-in x.
Q4:
Given the function
b(x+y)² -2<x< 2
elsewhere
Q5:
£x. y(x, y) = { b(x + y)²
and -3<y<3
(a) Find the constant b such that this is a valid joint density function.
(b) Determine the marginal density functions fx(x) and fy(y).
Two random variables X and Y have a joint density
fx, y(x, y)=[u(x)- u(x-4)]u(y) y³ exp[-(x + 1) y²]
Find the marginal densities and distributions of X and Y.
Transcribed Image Text:Q1: The random variable x is N (5, 2) and y = 2x+4. Find ny, oy, and fy(y). Q2: Find F, (y) and fy(y) if y = -4x+3 and fx(x) = 2e-²xU(x). Q3: The random variable x is uniform in the interval (0, 1). Find the density of the random variable y-in x. Q4: Given the function b(x+y)² -2<x< 2 elsewhere Q5: £x. y(x, y) = { b(x + y)² and -3<y<3 (a) Find the constant b such that this is a valid joint density function. (b) Determine the marginal density functions fx(x) and fy(y). Two random variables X and Y have a joint density fx, y(x, y)=[u(x)- u(x-4)]u(y) y³ exp[-(x + 1) y²] Find the marginal densities and distributions of X and Y.
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