3. Random variables X and Y have joint PDF fx.x(r, y) = { S 4xy 0
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Chapter1: Combinatorial Analysis
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I send for 3.question but you answered only a and b
![1. Random variables X and Y have joint PDF
fx,y(x, y) = { cry“ 0<x<1,0 < y < 1
otherwise
a) Find the constant c.
b) Find Pr{X >Y} and Pr{Y < X²}.
c) Find Pr{min(X,Y) < 1/2}.
d) Find Pr{max(X,Y)< 3/4}.
2. Random variables X and Y have joint PDF
fx.x(x, y) = {|
cx 0<x < 1,0 < y < 1
otherwise
%3D
a) Find the constant c.
b) Find the marginal PDF fx(x).
c) Are X andY independent? Justify your answer.
3. Random variables X and Y have joint PDF
fx.y(x, y) = { day 0<x<1,0< y <1
otherwise
a) What are E[X] and Var[X]?
b) What are E[Y] and Var[Y]?
c) What is Cov[X,Y]?
d) What is E[X +Y] ?
e) What is Var[X +Y] ?
4. If X has an exponential (A) PDF, what is the PDF of W = X² ?
5. X and Y have joint PDF
fxx(x, y) = {
S (x +y)/3 0< x < 1,0 < y < 2,
otherwise
Let A = {Y < 1}.
a) What is Pr{A} ?
b) Find fx.y|a(x, y).
c) Find fx|a(x) and fy|a(y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3cb2437-3187-4e88-8b36-293b5c4e2e05%2Fa3b319e4-d173-4e26-af1f-62fdf852d4d3%2F3jl6wem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Random variables X and Y have joint PDF
fx,y(x, y) = { cry“ 0<x<1,0 < y < 1
otherwise
a) Find the constant c.
b) Find Pr{X >Y} and Pr{Y < X²}.
c) Find Pr{min(X,Y) < 1/2}.
d) Find Pr{max(X,Y)< 3/4}.
2. Random variables X and Y have joint PDF
fx.x(x, y) = {|
cx 0<x < 1,0 < y < 1
otherwise
%3D
a) Find the constant c.
b) Find the marginal PDF fx(x).
c) Are X andY independent? Justify your answer.
3. Random variables X and Y have joint PDF
fx.y(x, y) = { day 0<x<1,0< y <1
otherwise
a) What are E[X] and Var[X]?
b) What are E[Y] and Var[Y]?
c) What is Cov[X,Y]?
d) What is E[X +Y] ?
e) What is Var[X +Y] ?
4. If X has an exponential (A) PDF, what is the PDF of W = X² ?
5. X and Y have joint PDF
fxx(x, y) = {
S (x +y)/3 0< x < 1,0 < y < 2,
otherwise
Let A = {Y < 1}.
a) What is Pr{A} ?
b) Find fx.y|a(x, y).
c) Find fx|a(x) and fy|a(y).
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