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In: Finance
Suppose that X and Y are two normally distributed random variables. X has mean 2 and...
Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation 3.Y has mean 3 and standard deviation 2. Their correlation is 0.6
. What is the mean and standard deviation of X + Y ?What is the distribution of X + Y ? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed?
Explain your answer.
Solutions
jeff jeffy answered 2 years agoRelated Solutions
Suppose that X and Y are two normally distributed random variables. X has mean 2 and...
Suppose that X and Y are two normally distributed random
variables. X has mean 2 and standard deviation 3.Y has mean 3 and
standard deviation 2. Their correlation is 0.6
. What is the mean and standard deviation of X + Y? What is the
distribution of X + Y? What if X and Y are jointly normally
distributed? What if they are not jointly normally distributed?
Explain your answer. (Why we cannot conclude if they are not
jointly normally...
Suppose that z = xy, where x and y are independent and normally distributed random variables
Suppose that z = xy, where x and y are independent and normally distributed random variables. The mean and variance of x are µx = 10 and σ2x = 2. The mean and variance of y are µy = 15 and σ2y = 3. Find the mean and variance of z by simulation. Does µz = µxµy? Does σ2z = σ2x σ2y? Do this for 100, 1000, and 5000 trials.
Suppose that y = x2, where x is a normally distributed random variable with a mean
Suppose that y = x2, where x is a normally distributed random variable with a mean and variance of µx = 0 and σ2x = 4. Find the mean and variance of y by simulation. Does µy = µ2x? Does σy = σ2x? Do this for 100, 1000, and 5000 trials.
8-5 (30) X and Y are independent random variables, and both are normally distributed with mean...
8-5 (30) X and Y are independent random variables, and both are
normally distributed with mean zero and variance one. Two new
random variables. Z and W are defined by Z = X2 +
Y2 , W = X/Y
(14) a). Find fz.w(z.w)indicating the domains over
which it is defined.
(10) b) Find the marginal densities fW (w) and
fZ (z) and the domain of each.
(6) c) Are Z and W independent? Explain
8-5 (30) X and Y are independent random variables, and both are normally distributed with mean...
8-5 (30) X and Y are independent random variables, and both are
normally distributed with mean zero and variance one. Two new
random variables. Z and W are defined by Z = X2 +
Y2 , W = X/Y
(14) a). Find fz.w(z.w)indicating the domains over
which it is defined.
(6) b). Are Z and W independent? Explain your answer.
(10) c) Find the marginal densities fW (w) and
fZ (z) and the domain of each.
A: Suppose two random variables X and Y are independent and identically distributed as standard normal....
A: Suppose two random variables X and Y are independent and
identically distributed as standard normal. Specify the joint
probability density function f(x, y) of X and Y.
Next, suppose two random variables X and Y are independent and
identically distributed as Bernoulli with parameter 1 2 . Specify
the joint probability mass function f(x, y) of X and Y.
B: Consider a time series realization X = [10, 15, 23, 20, 19]
with a length of five-periods. Compute the...
A random variable X is Normally distributed with mean = 75 and = 8. Let Y...
A random variable X is Normally distributed with mean = 75 and =
8. Let Y be a second Normally distributed random variable with mean
= 70 and = 12. It is also known that X and Y are independent of one
another. Let W be a random variable that is the difference between
X and Y (i.e., W = X – Y). What can be said about the distribution
of W?
Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y ,...
Question 1: Two jointly distributed discrete random variables
Consider two discrete random variables X, Y , taking values in {0,
1, 2, 3} each (for a total of 16 possible points). Their joint
probability mass function is given by fXY (x, y) = c · x+1 y+1 .
Answer the following questions. (a) What is c? (b) What is the
probability that X = Y ? (c) Derive the marginal probability mass
functions for both X and Y . (d)...
Let X and Y be two independent random variables such that X + Y has the...
Let X and Y be two independent random variables such that X + Y
has the same density as X. What is Y?
1. Suppose that the random variable X is normally distributed with mean μ = 30 and...
1. Suppose that the random variable X is normally distributed
with mean μ = 30 and standard deviation σ = 4. Find a) P(x < 40)
b) P(x > 21) c) P(30 < x < 35) 2. A radar unit is used to
measure speeds of cars on a motorway. The speeds are normally
distributed with a mean of 90 km/hr and a standard deviation of 10
km/hr. What is the probability that a car picked at random is
travelling...
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