Joint and Marginal Probability Density Functions of Independent Variables

Let X, Y be independent, standard normal random variables, and let U = X + Y and V = X - Y.
(a) Find the joint probability density function of (U, V) and specify its domain.
(b) Find the marginal probability density function of U and V specifying the domain in each case.
(c) Explain why U and V are independent

Joint probability density function of X and Y is given by
f(x,y)=6/7 (x^2+xy/2) 0<x<1. 0<y<2, Find P{X>Y} how to get the answer of 15/56?

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As X and Y are independent, standard normal random variables, their joint pdf f(x,y) is

A fair coin is tossed four times and X is number of heads on first three tosses and Y on last three. What is the jointprobability mass function of x and y? What is the marginal pmf? Are X and Y independent?

4.17. X has the U(?pi/2, pi/2) distribution, and Y = tan(X). Show that V has density l/(pi(1 + y2)) for ?oo density function.) What can be said about the mean and variance of Y? How could you simulate values from this distribution, given a supply of U(O, 1) values?
4.21. Let X and Y have joint den

1. Given the jointdensity function for the random variables X and Y as
The marginal distribution for the random variable X is
Answer:
2. Given the jointdensity function for the random variables X and Y as
The marginal distribution for the random variable Y is
Answer:
3. The following repr

Determine the value of c that makes the function f(x,y) = c(x+y) a jointprobabilitydensity function over the range:
x greater than 0 and less than 3 and x less than y less than x+2
a) P(X<1, Y<2)
b) P(11)
d) P(X<2, Y<2)
e) E(X)
f) V(X)
g) Marginalprobability distribution of X
h) Conditional probabilit

If A and B are independent events with P(A) = 0.25 and P(B) = 0.60, then P(A/B) is?
2. Intentions of customers regarding future automobile purchases and the financial capability of the consumers are given below:
Plan to buy
qualify for within 6 6 months or

1. If the moment generating function ( mgf ) of X is
(a) Find the mean of X.
(b) Find the variance of X.
(c) Find the pdf of X.
2. The jointprobability mass function for random variables X and Y is:
FXY (x, y) =(x + y)/32; x = 1, 2; y = 1, 2, 3, 4
(a) Show that fXY is a valid mass function.
(b) Find the mar

The joint density of X and Y is given by
f(x,y)= {xe to the power -(z+y) x>0, y>0
0 otherwise.
Are X and Y independent? What if f(x,y) were given by
f(x,y)= {2 0