Question: A random variable X is defined by f X (x) = 4e -8|x| The random variable Y is related to X by Y = 4

A random variable X is defined by 

fX(x) = 4e-8|x|


The random variable Y is related to X by Y = 4 + 5X.

(a) Determine E[X], E[X2], and σ2x.

(b) Determine fY(y).

(c) Determine E[Y], E[Y2], and σ2y. (The result of part (b) is not necessary to do this part, although it may be used.)

Step by Step Solution

★★★★★

3.44 Rating (176 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a From Table 64 E X 0 E X 2 132 var X b By transformation of random variables the ... View full answer

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 Principles Communications Systems Questions!

Q:

The characteristic function of a random variable, X, is M X (jv) = (1 + v 2 ) -1 . Find the following: (a) The mean of X; (b) The variance of X; (c) The pdf of X;

Q:

A continuous random variable X is constrained to a peak magnitude M that is ? M (a) Show that the differential entropy of X is maximum when it is uniformly distributed, as shown by (b) Show that the...

Q:

A random variable X has the probability-density function where α is an arbitrary positive constant. (a) Determine the characteristic function M x (jv). (b) Use the characteristic...

Q:

1. (Random Variables Standard Numerical Characteristics: Joint Distributions). Let a pair of fair four-faced dice be tossed. Consider the random variables X,Y:S-R on the corresponding sample space...

Q:

Let X be a random variable and a, b be constants. 1. Show that E(aX+b) : = aE(X)+b 2. Show that V(ax + b) = aV(X) You can assume that X is either a discrete or continuous random variable.

Q:

The probability function of a discrete random variable X has the form f (x) = c(x2 + 2|x| + 1), x RX = {2,1, 0, 1, 2}, for a suitable constant c. (i) Find the value of c. (ii) Calculate E(X) and...

Q:

12. The failure rate (or hazard rate) function of a random variable X is defined by r (t ) = f (t ) , where f is the p.d.f. and F is the c.d.f. 1 - F(t (a) Show that the failure rate function for an...

Q:

Macroeconomics 1 Suppose that PrArt is decreasing for 0 0, s(x) = (1 -x/w)" (05xsu) Give simple formulae for (i) (ii) er (Note finite limiting age), (iii) 10P70; (iv) 40 5935 A certain group of lives...

Q:

Suppose that 12 people need to be given a blood test for a certain disease. Assume that each person has a 10% chance of having the disease, independently from person to person. Consider two different...

Q:

i am SUPER confused and i will venmo any person who answers this before 12 tonight (in 2 hours) $8 just comment your venmo i gotchuuu PLEASE Suppose that 12 people need to be given a blood test for a...

Q:

What prints to the screen as a result of running this code? college word = 1111 i print (word) = "Blue Ridge" while i

Q:

1.30 The overweight problem. The 2011 National Health Interview Survey by the National Center for Health Statistics (NCHS) provides weight categorizations for adults 18 years and older based on their...

Q:

If the price of, say, oranges has risen, does it follow that the price level has risen too? Explain your answer.

Q:

Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information. Figure P2.44 Vor

Q:

The takeoff speed for an Airbus A320 jetliner is 80 m/s. Velocity data measured during takeoff are as shown. t (s) ___________ v x (m/s) 0 .. 0 10 .. 23 20 .. 46 30 .. 69 a. Is the jetliners...

Q:

FIGURE P2.46 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the...

Q:

Suppose that Bigco is currently trading for $100 per share. The stock has an annual volatility of 90 percent and does not pay any dividends. The riskless interest rate is 3 percent. What is the value...

Q:

Our Chapter 6 discussions will focus on working capital and the financing decision, tell us your reaction to the following: In addition to the companies' high public recognition, they have good...

Q:

During the boom years 2010-2014, mutual fund manager Diana Saurus produced the following % rate of return: - Calculate the average return and standard deviation of Ms. Sauros's mutual fund. - Did she...