Question

X andY are distributions with the following:

ux = 1,
ox = 2;
Let U = 2X + Y + 1. Find the following.
(a) Hu.
My = 2,oy = 1.

Answer 1

To find the distribution of U, we can apply the rules of combining random variables. The mean of U is 6 and the standard deviation of U is sqrt(17).

Step-by-step explanation:

To find the distribution of U, we can apply the rules of combining random variables.

We know that U = 2X + Y + 1, and we have the distributions of X and Y.

Using the properties of mean and standard deviation, we can calculate the mean and standard deviation of U as follows:

1. First, find the mean of U: Hu = 2 * Hx + Hy + 1
2. Next, find the standard deviation of U: ou = sqrt((2^2)*ox^2 + oy^2)

Substituting the given values, we have Hu = 2*1 + 2*1 + 1 = 6, and ou = sqrt((2^2)*(2^2) + 1^2) = sqrt(17). Therefore, the mean of U is 6 and the standard deviation of U is sqrt(17).