Question: Let X be a continuous random variable with pdf f(x). Suppose f(x) is symmetric about a; i.e., f(x a) = f((x a)). Show

Let X be a continuous random variable with pdf f(x). Suppose f(x) is symmetric about a; i.e., f(x − a) = f(−(x − a)). Show that the random variables X − a and −(X − a) have the same pdf.

Step by Step Solution

★★★★★

3.34 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Proof that the random variables X a and X a have the same pdf Since a was arbitrary we have that ... View full answer

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!

Let X be a continuous random variable with values in [0, 2] and density fX. Find the moment generating function g(t) for X if (a) fX(x) = 1/2. (b) fX(x) = (1/2)x. (c) fX(x) = 1 (1/2)x. (d) fX(x) = |1...

Let X be a continuous random variable with values in [0,) and density fX. Find the moment generating functions for X if (a) fX(x) = 2e2x. (b) fX(x) = e2x + (1/2)e-x. (c) fX(x) = 4xe2x. (d) fX(x) = (...

Let X be a continuous random variable with values in [0, 1], uniform density function fX(x) 1 and moment generating function g(t) = (et 1)/t. Find in terms of g(t) the moment generating function for...

Problem 4 Let X be any continuous random variable with pdf f (x). Find the pdf of I X l. Problem 5 Let X, Y iid Exponential(,\) (a) Define T := X + Y, R := X/ Y. Use the Jacobian method to find the...

Let X be a continuous random variable with pdf given by f( x) = 10 Jx/2 0 5x 52 otherwise Find E[ X]. Report answer to 4 decimal places. Question 2 Let X be a continuous random variable with pdf...

4. For each statement below, determine whether the statement is true or false. Circle your answer if you are writing your solutions on this document. If you are writing your solutions in a separate...

Let X be a continuous random variable with CDF F and PDF f. (a) Find the conditional CDF of X given X > a (where a is a constant with P(X > a) # 0). That is, find P(X a) for all a, in terms of F. (b)...

Let X be a continuous random variable with a pdf function f(x) that is symmetric around 0 (i.e. f(x) = f(-x) for every x). Compute the probability that X > 0 A: 1/2 B: Cannot be known; depends on the...

More on expected value Because the expected value concept plays an important role in many economic theories, it may be useful to summarize a few more properties of this statistical measure....

9. Let X be a continuous random variable with probability density function f.We say that X is symmetric about if for all x, (a) Prove that X is symmetric about if and only if for all x, we have f( ...

Find the cost of 200 suits if 75 suits cost $10,200.

Multinational enterprises do not formulate worldwide strategies but rather regional strategies. What does this statement mean and how does it help us better understand international business?

Hals Heavenly Creations oflers its employtes the option of contributing up to 7 Th of their salaries to a voluntary retinement plan, wich the employer matching their contribution. The compaty Wlsb...

Which of the motivational theories do you prefer? Why?

Set up and carry out an appropriate hypothesis test for the Hanford radioactive contamination data given in Question 11.2.9. Let = 0.05. Justify your choice of H0 and H1. What do you conclude?

Test H0: 1 = 0 versus H1: 1 = 0 for the plumage index/behavioral index data given in Question 11.2.11 Let = 0.05. Use the fact that y = 0.61 + 0.84x is the best straight line describing the...

Let X and Y have the joint pdf Find Cov(X, Y ) and (X, Y ). 1222, 0, for (x, y):: (1,1), (1,3), (2.1), (23) elsewhere fx.Y (x , y)

Question 11 (0.2 points) A firm has an effective (after-tax) cost of debt of 4%, and its weight of debt is 40%. Its equity cost of capital is 9%, and its weight of equity is 60%. Calculate the firm's...

Mr et Mme Durand ont pu emprunter une somme de 50 000 $ auprs de leur banque RBC banque. Ils ont achet une voiture pour 30 000 $ chez le concessionnaire Buzzarello, client de la RBC banque. Ils ont...

Greta has risk aversion of A=5 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies....