Question: Let X and Y be independent random variables. Given that the variance of X is 3, and the variance of Y is 3, find the

Let X and Y be independent random variables.

Given that

the variance of X is 3, and

the variance of Y is 3,

find the variance of the random variable Z=5X+2Y+93.


Step by Step Solution

★★★★★

3.40 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Question 1 Suppose you are a senior portfolio manager of an international investment bank that oversees a US investment portfolio with total assets of 28 billion. For company B&G Ltd., you know the...

Q:

Let X and Y be independent random variables with uniform densities in [0, 1]. Let Z = X + Y and W = X Y. Find (a) p (X, Y ) (see Exercise 18). (b) p (X,Z). (c) p (Y,W). (d) p (Z,W).

Q:

Let X and Y be independent random variables with uniform densities in [0, 1]. Let Z = X + Y and W = X Y. Find (a) p (X, Y ) (see Exercise 18). (b) p (X,Z). (c) p (Y,W). (d) p (Z,W).

Q:

Let X and Y be independent random variables with X = 2, X = 1, Y = 2, and Y = 3. Find the means and variances of the following quantities. a. 3X b. X + Y c. X Y d. 2X + 6Y

Q:

Let X 1 and X 2 be independent random variables having the uniform density with = 0 and = 1. Referring to Figure 7.2, find expressions for the distribution function of Y = X1 + X2 for (a) y 0; (b)...

Q:

Let X and Y be independent n(0,1) random variables, and define a new random variable Z by (a) Show that Z has a normal distribution. (b) Show that the joint distribution of Z and Y is not bivariate...

Q:

9.16. Let X1 and X2 be independent random variables each having distribution Nu, 2). Let Z(t) = X cos wt + X2 sin cof. This random variable is of interest in the study of random signals. Let V(t) =...

Q:

Let X1 and X2 be independent random variables each having the probability distribution f(x) = ex, x> 0, 0, elsewhere. Show that the random variables Y1 and Y2 are independent when Y1 = X1 + X2 and Y2...

Q:

Let X1 and X2 be independent random variables and let Y1 = Ф1(X1) and Y2 = Ф2(X2). (a) Show that (b) Using (a), show that P (Y1 = r, Y2 = s) = P (Y1 = r) P (Y2 = s) so that Y1 and Y2 are...

Q:

Let X 1 and X 2 be independent random variables each having the probability distribution show that the random variables Y 1 and Y 2 are independent when Y 1 = X 1 + X 2 and Y 2 ? X 1 (X +X 2 ). x>0....

Q:

Let X1 and X2 be independent random variables with respective binomial distributions b(3, 1/2) and b(5, 1/2). Determine (a) P(X1 = 2, X2 = 4). (b) P(X1 + X2 = 7).

Q:

The following transactions apply to Hooper Company for Year 1, Its first year of operations: 1. Issued $110,000 of common stock for cash. 2. Provided $104,000 of services on account. 3. Collected...

Q:

Determine whether the planes are parallel. (a) 4x - y + 2z = 5 and 7x - 3y + 4z = 8 (b) x - 4y - 3z - 2 = 0 and 3x - 12y - 9z - 1 = 0

Q:

Let f and g b e functions that satisfy f ' ( 2 ) = 1 0 and g ' ( 2 ) = 1 . Find h ' ( 2 ) for each function h given belo ( A ) h ( x ) = 8 f ( x ) . h ' ( 2 ) = ( B ) h ( x ) = - 5 g ( x ) . h ' ( 2...

Q:

Joseph contributed $23,750 in cash and equipment with a tax basis of $13,700 and a fair market value of $17,400 to Berry Hill Partnership in exchange for a partnership interest. a. What is Joseph's...

Q:

Identify the type of organic compound shown: H;C-C-CH;CH, O aldehyde Oester (o amine Oalcohol O none of these

Q:

Evaluate the limit. (If you need to use -o or o, enter -INFINITY or INFINITY.) sin (8 r) lim 10 tan (9 a)

Q:

Ramon incorporated his sole proprietorship by transferring inventory, a building, and land to the corporation in return for 100 percent of the corporation's stock. The property transferred to the...

Q:

Orthogonally diagonalize the matrix 4 3 1 1 3 4 1 1 A = I 1 4 3 1 3 4 knowing that its eigenvalues are 1, 5 and 9.

Q:

Cuddy, M. F., & Fisher, E. R. (2010). Investigation of the roles of gas-phase CF2 molecules and F atoms during fluorocarbon plasma processing of Si and ZrO2 substrates. Journal of Applied Physics,...

Q:

Let X and Y be independent random variables with X having the t distribution with five degrees of freedom and Y having the t distribution with three degrees of freedom. We are interested in E(|X Y...

Q:

Let X1, X2, . . . ,Xn be independent random variables having an unknown continuous distribution function F, and let Y1,Y2, . . . ,Ym be independent random variables having an unknown continuous...

Q:

Consider the density function of a random variable X defined by (a) Find the CDF corresponding to this density function. (Be sure you describe it completely.) (b) Calculate the mean and variance. (c)...

Q:

Let X be a random variable taking on values a1, a2, . . . , pr with probabilities p1, p2, . . . , pr and with E(X) = μ. Define the spread of X as follows: This, like the standard deviation, is a...

Q:

Let X, Y, and Z be independent random variables, each with mean and variance 2. (a) Find the expected value and variance of S = X + Y + Z. (b) Find the expected value and variance of A = (1/3) (X + Y...

Q:

Let X, Y, and Z be independent random variables, each with mean and variance 2. (a) Find the expected value and variance of S = X + Y + Z. (b) Find the expected value and variance of A = (1/3) (X + Y...