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In: Statistics and Probability
Question 3: Independent or not? For the following four joint probability distributions of X and Y...
Question 3: Independent or not? For the following four joint probability distributions of X and Y , either prove or disprove that X and Y are independent. 1. fXY (x, y) = λ 2 e −λ(x+y) , x, y ≥ 0. 2. fXY (x, y) = 6 5 x + y 2 , 0 ≤ x, y ≤ 1. 3. fXY (x, y) = 1 9 xy, 0 ≤ x ≤ 3, and 0 ≤ y ≤ 2. 4. fXY (x, y) = 8xy, 0 ≤ x ≤ y ≤ 1.
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orchestra answered 2 years agoRelated Solutions
Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0...
Question 3
Suppose that X and Y have the following joint probability
distribution:
f(x,y)
x
0
1
2
y
0
0.12
0.08
0.06
1
0.04
0.19
0.12
2
0.04
0.05
0.3
Find the followings:
E(Y)=
Var(X)=
Cov(X,Y)=
Correlation(X,Y)=
Suppose the joint probability distribution of X and Y is given by the following table. Y=>3...
Suppose the joint probability distribution of X and Y is given
by the following table.
Y=>3 6 9 X
1 0.2 0.2 0
2 0.2 0 0.2
3 0 0.1 0.1
The table entries represent the probabilities. Hence the
outcome [X=1,Y=6] has probability
0.2.
a) Compute E(X), E(X2), E(Y), and E(XY). (For all answers show
your work.) b) Compute E[Y | X = 1], E[Y | X = 2], and E[Y | X =
3].
c) In this case, E[Y...
9.8 Let X and Y be independent random variables with probability distributions given by P(X =...
9.8 Let X and Y be independent random variables with probability
distributions given by
P(X = 0) = P(X = 1) = 1/2 and P(Y = 0) = P(Y = 2) = 1/2 .
a. Compute the distribution of Z = X + Y .
b. Let Y˜ and Z˜ be independent random variables, where Y˜ has
the same distribution as Y , and Z˜ the same distribution as Z.
Compute the distribution of X˜ = Z˜ − Y
Stocks X and Y have the following probability distributions of expected returns for four possible economic...
Stocks X and Y have the following probability distributions of
expected returns for four possible economic states.
Economy State
Probability
Stock X
Stock Y
1
0.1
-8%
5%
2
0.4
-10%
8%
3
0.4
9%
-2%
4
0.1
14%
-10%
e. Calculate the two-stock portfolio’s standard deviation.
f. Calculate the two-stock portfolio’s beta.
g. If the overall market return is 8% and the risk-free rate is
1%, what is the two-stock portfolio’s required return?
h. How can you reallocate t
Stocks X and Y have the following probability distributions of expected returns for four possible economic...
Stocks X and Y have the following probability distributions of
expected returns for four possible economic states.
Economy State
Probability
Stock X
Stock Y
1
0.1
-8%
5%
2
0.4
-10%
8%
3
0.4
9%
-2%
4
0.1
14%
-10%
Suppose you construct a two-stock portfolio that has $3 million
invested in Stock X and $1 million invested in Stock Y. The beta of
Stock X is 20% higher than the beta of overall stock market. Stock
Y’s beta is...
Given the following probability distributions for variables X and Y: P(x, y)X Y 0.4 100 &
Given the following probability distributions for variables X
and Y:
P(x,
y)X Y
0.4 100 200
0.6 200 100
a. E(X) and E(Y).
b. σX and σY.
c. σXY. d. E(X + Y).
e. Suppose that X represents the number of patients successfully
treated for Malaria and Y represents the number of patients
successfully treated for Tuberculosis. And medication A (first row
in the table) has a 40% of effectiveness and medication B (second
row in the table) has a 60% of effectiveness. Interpret and...
Stocks X and Y have the following probability distributions of expected future returns: Probability X Y 0.3 &nb
Stocks X and Y have the following probability distributions of
expected future returns:
Probability X Y
0.3 2% 25%
0.4 12% 20%
0.3 20% 0%
One investor invests 40% in stock X and 60% in stock Y. Calculate
the expected return, standard deviation, and coefficient of
variation Stocks X and Y. Compute the expected rate of return for
the portfolio.
Stocks X and Y have the following probability distributions of expected future returns: Probability X Y 0.3 &nb
Stocks X and Y have the following probability distributions of
expected future returns:
Probability X Y
0.3 2% 25%
0.4 12% 20%
0.3 20% 0%
One investor invests 40% in stock X and 60% in stock Y. Calculate
the expected return, standard deviation, and coefficient of
variation Stocks X and Y. Compute the expected rate of return for
the portfolio.
If the joint probability distribution of X and Y f(x, y) = (x + y)/2
If the joint probability distribution of X and Y f(x, y) = (x + y)/2, x=0,1,2,3; y=0,1,2, Compute the following a. P(X≤2,Y =1) b. P(X>2,Y ≤1) c. P(X>Y) d. P(X+Y=4)
Suppose that X and Y have the following joint probability density function. f (x, y) =...
Suppose that X and Y have the following joint probability
density function. f (x, y) = (3/394)*y, 0 < x < 8, y > 0,
x − 3 < y < x + 3
(a) Find E(XY). (b) Find the covariance
between X and Y.
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