Question: For any positive number k, verify that f (x) = 1/(2k 3 )x 2 e -x/k , x 0, is a density function.

For any positive number k, verify that f (x) = 1/(2k3)x2 e-x/k, x ≥ 0, is a density function.

Step by Step Solution

★★★★★

3.37 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

I If k 0 1 273 xk0 for a... 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 Applied Calculus Questions!

Q:

Suppose where is some positive constant with the appropriate dimensions. Wed like to find the bound statessolutions to the time-independent Schrdinger equation with negative energy (E

Q:

For the JVP y' = y. y (0) = 0 of Example 3, and for any positive number t0 show that a solution is given by equation (4).

Q:

For any non-zero number a, one can explain why a = 1 by the rules of exponents. 1 = a +a" = a"-" = a Explain why a-1 for any non-zero number a. (Don't just say "it is a rule", but you may want to use...

Q:

M Inbox (9,036) - brando x o Mail - Brandon C Arch X Section 5.1 X P Do Homework - Sectic X Course Hero X Mathway | Algebra Prc X C Home | Chegg.com X + X CA...

Q:

pleaseanswerthese (1 point) Encrypt the message " HALT " by translating the letters into numbers (via A = 0, B = 1, C = 2, D = 3, E = 4, F = 5, G = 6, H = 7, 1 = 8, J = 9, K = 10, L = 11, M = 12, N =...

Q:

(1) Consider the function f : R' - R given by zk (exty - 1 ) if ( x, y, z) # (0, 0, 0), f ( x, y, Z ) = 3 (x 2 + 2 + z2) k 0 if (x, y, Z) = (0, 0, 0), where k is a positive constant. (a) Find all...

Q:

3.1 Higher Order Derivatives. Velocity and Acceleration 1 . Find f' , f" , f" , f ( 4 ) , f (5 ) , f ( 6 ) for f ( x ) = x5 + x 3 - x 2 + x + 2 . 2. Find f' and f" for f(x) = V1-x2 . Write the...

Q:

In MATLAB can you write these three codes. A method that overloads ?. Suppose P1 and P2 are objects of class MyPolynomial and c is a numeric scalar. This method should support the following...

Q:

At Elproparts Manufacturers integrated circuit business, managers gathered data from a customer focus group and found that any output voltage that exceeds 60 ` 3.5 volts was unacceptable to the...

Q:

3.1 Higher Order Derivatives. Velocity and Acceleration 1 . Find f' , f" , f" , f ( 4 ) , f (5 ) , f ( 6 ) for f ( x ) = x5 + x 3 - x 2 + x + 2 . 2. Find f' and f" for f(x) = V1-x2 . Write the...

Q:

A company is evaluating a new 4-year project. The equipment necessary for the project will cost $3,200,000 and can be sold for $685,000 at the end of the project. The asset is in the 5-year MACRS...

Q:

Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the...

Q:

2.55 The file New Home Sales contains the number of new homes sold (in thousands) and the median sales price of new single-family houses sold in the United States recorded at the end of each month...

Q:

A discrete random variable X has a Bernoulli distribution with parameter p = 0.3. Using the following uniform variates, generate Bernoulli variates using Equation 7.20. Determine the sample...

Q:

An article in Biotechnology Progress (2001, Vol. 17, pp. 366368) reported on an experiment to investigate and optimize nisin extraction in aqueous two-phase systems (ATPS). The nisin recovery was the...

Q:

An article in Optical Engineering [Operating Curve Extraction of a Correlators Filter (2004, Vol. 43, pp. 27752779)] reported on the use of an optical correlator to perform an experiment by varying...

Q:

Table E12-11 presents quarterback ratings for the 2008 National Football League season (The Sports Network). (a) Fit a multiple regression model to relate the quarterback rating to the percentage of...

Q:

IB (True/False) 6. (1 point) Canada attracts international investment by building clusters of industries, such as high-tech industries. 7. (I point) The business decisions that a company makes about...

Q:

Mickley Corporation produces two products, Alpha6s and Zeta7s, which pass through two operations, Sintering and Finishing. Each of the products uses two raw materialsX442 and Y661. The company uses a...

Q:

As an audit assistant you are on the audit team assigned to audit, BP, you are working on the 2015 audit. The following are the financial statements that have been submitted by the Chief financial...