6)h and g. Solve them step by step. 6)- Let x and y have the joint densityf(x, y) = {* + cy if 15x< 2;0

X and Y are independent iff f(x,y)=f(x) f(y) Cov(x,y)=E(xy)-E(x)E(y)

Answered: 6)- Let x and y have the joint density…

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6)- Let x and y have the joint density f(x, y) = {* + cy if 15x< 2;0

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

6) h and g. Solve them step by step.

6)- Let x and y have the joint density
f(x, y) = {* + cy if 15x< 2;0<ys1
elsewhere
where c is a constant
a) Find the value of c that makes f(x, y) a probability density function.
b) Find the marginal density for y and show that
O)dy = 1
c) Find f1(xly), the conditional density for x given y.
d) Find E(x)
e) Find E(y)
f) Find E(x + y)
g) Are x and y independent?
h) Find the covariance of the random variables x and y.

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