Question: Let X have the exponential pdf, f(x) = 1 exp{x/}, 0 < x < , zero elsewhere. Find the mgf, the mean, and the variance

Let X have the exponential pdf, f(x) = β−1 exp{−x/β}, 0 < x < ∞, zero elsewhere. Find the mgf, the mean, and the variance of X.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To solve this problem well find the momentgenerating function mgf mean and variance for a random var... 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 Mathematics Questions!

Q:

Let X have the exponential distribution with parameter . Suppose that we wish to test the hypotheses H0: = 1, H1: = 1. We shall use a test procedure that rejects H0 if either X c1 or X c2. a....

Q:

Let X have the exponential distribution with parameter . Prove that the median absolute deviation of X is smaller than one-half of the IQR. (You can do this without actually calculating the median...

Q:

Let X have the exponential distribution with parameter . Suppose that we wish to test the hypotheses H0 : 1 versus H1 :

Q:

solve the question HOW People Getl heir News The Brunswick Research Organization surveved 50 randomly,r selected individuals and asked them the pmal'f wag.r they received the daily news. Their...

Q:

Let X have the probability density function (pdf) Cx(e " te 2* +e- 3x), ifx>0, fx (20) = 0, otherwise. (a) Find the normalizing constant C and moment generating function (mof ) of X. (b) Find the cdf...

Q:

The Beta distribution with parameters a = 3, b = 2 has PDF f(x)=12x 2 (1x), for 0

Q:

1. For each 0! the lol lowing exercises. determine the range {output. possible values} oi the random variable. {a} A group of 1,000 people is tested [or 0 FthD negative blood type. The random...

Q:

Answer all of the following Question Three Suppose that two balanced dice are rolled. Determine and sketch the probability distribution of each of the following random variables. 1. Let X denote the...

Q:

========================================================================== (Problem 1) A random sample of 12 customers was chosen in a supermarket. The (incomplete) results for their checkout times...

Q:

Please provide the python code 4. (Coding) Let X be an exponential random variable Exp(a), so that the probability density function is f(x) = leds, for 2 > 0. Recall that the mean is p = 1/2 and the...

Q:

LAB 1 CREATE TABLE EMPLOYEE(EMP_ID INT PRIMARY KEY, EMP_NAME VARCHAR(20),EMP_AGE INT,SALARY INT); CREATE TABLE DEPENDENTS(DEPNDT_NAME VARCHAR(20),EMP_ID INT,DEPNDT_AGE INT,FOREIGN...

Q:

Smoothing constant in the Nave method is (a) 0.2 to 0.5 (b) 0.5 to 0.7 (c) 1 (d) None of these

Q:

Find the sum o f the series n = 1 1 2 n 1 2 correct t o three decimal places. Step 1 Consider that f ( x ) = 1 2 x 1 2 i s positive and continuous for x > 0 . T o decide i f f ( x ) = 1 2 x 1 2 i s...

Q:

Grantham Manufacturing Company makes oak racing chairs. Budgeted sales are 19,600 for July, 25,900 for September and 31,600 for October. Grantham maintains an ending inventory equal to 10% of the...

Q:

Craig Manufacturing Company's budgeted income statement includes the following data: Data extracted from budgeted income statement Mar Apr May Jun Sales $120,000 $90,000 $95,000 $100,000 Commission...

Q:

A manufacturing company's budgeted income statement includes the following data: The budget assumes that 60% of commission expenses are paid in the month they were incurred and the remaining 40% are...

Q:

A manufacturing company's budgeted income statement includes the following data: The budget assumes that 60% of commission expenses are paid in the month they are incurred and the remaining 40% are...

Q:

Income statement for the financial year ended March 31for Fiona Frolickers is as follows: A. Perform horizontal analysis on the income statement. Round to closest percent (e.g 36.5% to 37%). B....

Q:

Japan: Opportunity cost of 1 car: Opportunity cost of 1 ton of grain: make this as 1 paragraph

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

Let f(x, y) = (2/ 2 )e (x+y) / , 0

Q:

The two-parameter exponential distribution uses a different range for the random variable X, namely, 0 x for a constant (and this equals the usual exponential distribution in the special case...

Q:

Analyze the financial performance and financial condition of Palomar Health. ProviderecommendationstotheboardofdirectorsabouthowPalomarHealthcanachieveisstrategicobjectiveswithfinancialsuccess. APA,...

Q:

Statistics and probability, help. Exercise 17 (#2.40). Let (X1. .... X,), n > 2, be a random sample from a distribution having Lebesgue density fo,,, where # > 0, j = 1, 2, fo,1 is the density of...

Q:

44. Component lifetimes have the exponential distribution with pdf f (x; l) lelx, x 0, and f (x; l) 0 otherwise, where l 0. However, we wish to estimate the mean m1/l based on the random sample...