Exercise 10.45. Suppose that the joint distribution of X,Y is
bivariate normal with parameters σX,σY,ρ,µX,µY as...
Exercise 10.45. Suppose that the joint distribution of X,Y is
bivariate normal with parameters σX,σY,ρ,µX,µY as described in
Section 8.5. (a) Compute the conditional probability density of X
given Y =y. (b) Find E[X|Y].
Let X and Y be two independent random variables with
μX =E(X)=2,σX =SD(X)=1,μY =2,σY =SD(Y)=3.
Find...
Let X and Y be two independent random variables with
μX =E(X)=2,σX =SD(X)=1,μY =2,σY =SD(Y)=3.
Find the mean and variance of
(i) 3X
(ii) 6Y
(iii) X − Y
You have two random variables X and Y
X -> μX = 5 , σX =...
You have two random variables X and Y
X -> μX = 5 , σX = 3
Y -> μY = 7 , σY = 4
Now, we define two new random variables
Z = X - Y
W = X + Y
Answer the below questions:
μZ =
[ Select ]
["3",
"1", "-2"]
σZ =
...
Given a random variable X following normal distribution with
mean of -3 and standard deviation of...
Given a random variable X following normal distribution with
mean of -3 and standard deviation of 4. Then random variable
Y=0.4X+5 is also normal.
(1)Find the distribution of Y, i.e. μy,σy
(2)Find the probabilities P(−4<X<0),P(−1<Y<0)
(3)Find the probabilities(let n size =8)
P(−4<X¯<0),P(3<Y¯<4)
(4)Find the 53th percentile of the distribution of X
1. A and b are not correlated, treat as separate problems
a) The random variable X...
1. A and b are not correlated, treat as separate problems
a) The random variable X has uniform continuous distribution on
the interval [0, 10]. Find the distribution of Y = X3 and
P(Y > 50).
b) The random variables X and Y are jointly bivariate normal
with parameters µX = 0, σX = 1, µY = 0, σY = 2 and ρ = 0.9.
i) Find P(Y > 0)
ii) Find P(Y > 0|X = 1)
Given a random variable XX following normal distribution with
mean of -3 and standard deviation of...
Given a random variable XX following normal distribution with
mean of -3 and standard deviation of 4. Then random variable
Y=0.4X+5Y=0.4X+5 is also normal.
(1)(2pts) Find the distribution of YY, i.e. μY,σY.μY,σY.
(2)(3pts) Find the probabilities
P(−4<X<0),P(−1<Y<0).P(−4<X<0),P(−1<Y<0).
(3)(3pts) Find the probabilities
P(−4<X¯<0),P(3<Y¯<4).P(−4<X¯<0),P(3<Y¯<4).
(4)(4pts) Find the 53th percentile of the distribution of
XX.
Let (X1, Y1), . . . ,(Xn, Yn), be a random sample from a
bivariate normal...
Let (X1, Y1), . . . ,(Xn, Yn), be a random sample from a
bivariate normal distribution with parameters µ1, µ2, σ2 1 , σ2 2 ,
ρ. (Note: (X1, Y1), . . . ,(Xn, Yn) are independent). What is the
joint distribution of (X ¯ , Y¯ )?
Let the random variable X and Y have the joint pmf f(x, y) =
xy^2/c where...
Let the random variable X and Y have the joint pmf f(x, y) =
xy^2/c where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are
{(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} .
(a) Find c > 0 .
(b) Find μX
(c) Find μY
(d) Find σ^2 X
(e) Find σ^2 Y
(f) Find Cov (X, Y )
(g) Find ρ , Corr (X, Y )
(h) Are X...