Question: Show that the moment generating function of the random variable X having the pdf f(x) = 1/3 , 1 < x < 2, zero elsewhere,

Show that the moment generating function of the random variable X having the pdf f(x) = 1/3 , −1

M (t) = { e2t-e- 3t 1 t #0 t = 0.

M (t) = { e2t-e- 3t 1 t #0 t = 0.

Step by Step Solution

★★★★★

3.35 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Mt et3 We have Mt et3 Differentia... 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 Statistical Techniques in Business Questions!

Q:

A certain type of bacteria grows according to the function P (t) = 1,300e0.1722t, where P(t) is the number of bacteria present after t hours. Find the number of bacteria present after 6 hours. Enter...

Q:

The moment generating function of X is given by MX(t) = exp{2et 2} and that of Y by MY(t) = (3/4et + 1/4)10. If X and Y are independent, what are (a) P{X + Y = 2}? (b) P{XY = 0}? (c) E[XY]?

Q:

The probability density function of the random variable X is given by Find the expected value of the random variable X. 0

Q:

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

Q:

I NEED HELP ASAP.BE SURE TO ANSWER 3.64. (a) Find the moment generating function of a random variable X having density function (b) Use the generating function of (a) to find the first four moments...

Q:

{b} Suppose the moment generating function of the random variable X is Mr {t}. i. For any constants o. and b, show that the moment generating function of: Y = {IX + h is: MyEt} = \"Mxrag. [4 marks}...

Q:

The moment generating function of the random variable X having a chi squared distribution with v degrees of freedom is Mx t 1 2t show that the mean and variance of the chi squared distribution with v...

Q:

Given the RV X with the following pdf: f(x)= e^(-x+3)for x>3 and f(x)=0, otherwise: find the moment generating function of the random variable X. find the mean and variance X. What is the pdf of RV Y...

Q:

Find the moment generating function for a random variable X with probability density function f (x) = e ex if 0 x 1.

Q:

Probability Questions a~d (a) Let MX(t) = E(e tX) be the moment generating function of the random variable X. Show that \f

Q:

Your firm bought goods from an American firm for US$100,000 on 1/1/20X8. The settlement date is 1/2/20X8. Given the spot rate on 1/1/20X8 is US$1 = S$1.34 and 30-day forward rate is US$1 = S$1.35....

Q:

About Oman Cables or SALALAH MILLS or Sweets of Oman Look for financial statements of real-life companies with equity investments. Both local and international companies will be accepted. The...

Q:

6. What is Total Productive Maintenance?

Q:

describe and present a summary of data you have collected.

Q:

Electromagnetic fields generated by power transmission lines are suspected by some researchers to be a cause of cancer. Especially at risk would be telephone linemen because of their frequent...

Q:

Astronomers estimate that as many as one hundred billion stars in the Milky Way galaxy are encircled by planets. If so, we may have a plethora of cosmic neighbors. Let p denote the probability that...

Q:

State Tech's basketball team, the Fighting Logarithms, have a 70% foul-shooting percentage. (a) Write a formula for the exact probability that out of their next one hundred free throws, they will...

Q:

Question 19 (1 point) Listen XYZ Corp. pays a constant $7.80 dividend on its stock. The company will maintain this dividend for the next 11 years and will then cease paying dividends forever. If the...

Q:

Your parents will retire in 20 years. They currently have $290,000 saved, and they think they will need $1,650,000 ot retirement. What annual interest rate must they earn to reach their goal,...

Q:

The balance sheet of XYZ Bank appears below. All figures in millions of US Dollars. TOTAL ASSETS 970 TOTAL LIABILITIES \& EQUIT Suppose that interest rates rise by 2% on both Rate-Sensitive Assets...