Let X∼Γ(a1,b) be independent of Y, and suppose W=X+Y∼Γ(a2,b),
where a2> a1. ShowY∼Γ(a2−a1,b)
Let X∼Γ(a1,b) be independent of Y, and suppose W=X+Y∼Γ(a2,b),
where a2> a1. ShowY∼Γ(a2−a1,b)
Let X and Y denote the values of two stocks at the end of a 5...
Let X and Y denote the values of two stocks at the end of a 5
year-period. X is uniformly distributed on the interval (0, 10).
Given X=x, Y is uniformly distributed on the interval (0, 2x).
Determine Cov[X, Y] according to this model.
Let X and Y denote the values of two stocks at the end of a 5...
Let X and Y denote the values of two stocks at the end of a 5
year-period. X is uniformly distributed on the interval (0, 10).
Given X=x, Y is uniformly distributed on the interval (0, 2x).
Determine Cov[X, Y] according to this model.
Given the following five pairs of (x, y)
values,
x
5
3
10
7
14
y...
Given the following five pairs of (x, y)
values,
x
5
3
10
7
14
y
10
6
4
3
0
Determine the least squares regression line.
ANSWER correct to 4 decimal places
(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪
A2 ∪...
(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪
A2 ∪ ... ∪ An is countable. (Hint: Induction.)
(6) Let F be the set of all functions from R to R. Show that |F|
> 2 ℵ0 . (Hint: Find an injective function from P(R) to F.)
(7) Let X = {1, 2, 3, 4}, Y = {5, 6, 7, 8}, T = {∅, {1}, {4},
{1, 4}, {1, 2, 3, 4}}, and S =...
Let X and Y denote the values of two stocks at the end of a five...
Let X and Y denote the values of two stocks at the end of a five
year period. X is uniformly distributed on the interval (0,12).
Given X=x, Y is uniformly distributed on the interval (0,x).
Determine Cov(X,Y) according to the model.
Let x and Y be two discrete random variables, where x Takes
values 3 and 4...
Let x and Y be two discrete random variables, where x Takes
values 3 and 4 and Y takes the values 2 and 5. Let furthermore the
following probabilities be given:
P(X=3 ∩ Y=2)= P(3,2)=0.3,
P(X=3 ∩ Y=5)= P(3,5)=0.1,
P(X=4 ∩ Y=2)= P(4,2)=0.4 and
P(X=4∩ Y=5)= P(4,5)=0.2.
Compute the correlation between X and Y.
Let x and Y be two discrete random variables, where x Takes
values 3 and 4...
Let x and Y be two discrete random variables, where x Takes
values 3 and 4 and Y takes the values 2 and 5. Let furthermore the
following probabilities be given:
P(X=3 ∩ Y=2)= P(3,2)=0.3,
P(X=3 ∩ Y=5)= P(3,5)=0.1,
P(X=4 ∩ Y=2)= P(4,2)=0.4 and
P(X=4∩ Y=5)= P(4,5)=0.2.
Compute the correlation between X and Y.