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 f(x) = 2e-²xU(x). Q3: The random variable x is uniform in the interval (0, 1). Find the density of the randor variable y-in x. Q4: Given the function [b(x+y)² -2
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 f(x) = 2e-²xU(x). Q3: The random variable x is uniform in the interval (0, 1). Find the density of the randor variable y-in x. Q4: Given the function [b(x+y)² -2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prob ... solve Q 1 & Q 2 please ?
![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.x(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)²]
Find the marginal densities and distributions of X and Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a72475f-f236-47a3-b928-04aacc1e5dcb%2Ff17be0dc-1c81-4292-bed9-ca0200848143%2Foe2mnl_processed.jpeg&w=3840&q=75)
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.x(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)²]
Find the marginal densities and distributions of X and Y.
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