Let X 1 , , X n be independent log normal random variables and let a 1 , , an be constants Show that the product P X a 1 1 X a n n is lognormal ln P a 1 ln X 1 an ln X n

Question: Let X 1 , . . . , X n be independent log normal random variables and let a 1 , . . . ,

Let X₁, . . . , X_n be independent log normal random variables and let a₁, . . . , an be constants. Show that the product P = X^a₁¹· · · X^a_nⁿ is lognormal. ln P = a₁ ln X₁ +· · ·+an ln X_n.

Step by Step Solution

★★★★★

3.42 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ln X 1 ln X n are independent ... 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 Statistics Engineers Scientists Questions!

Let X1, . . ., Xn be independent and identically distributed random variables with pdf f(x) = (1 / )e x/, x > 0, y > 0. Find the pdf of -.

Let X1, . . . ,Xn be independent exponential random variables having a common parameter . Determine the distribution of min(X1, . . . ,Xn).

Let X1,..., Xn be independent random variables with pdfs where Î¸ > 0. Find a two-dimensional sufficient statistic for Î¸. -(r otherwise Uz,10) =

Let X and Y be two independent standard normal random variables. Consider the point (X,Y ) in the x y plane. Let (R,) be the corresponding polar coordinates as shown in Figure 5.11. The inverse...

Let X and Y be two independent standard normal random variables, and let Z = X +Y. Find the PDF of Z.

Let X u...,Xn be independently and identically distributed normal random variables with mean |x and variance a 2. (a) Show that is an n x n idempotent matrix of rank n - 1 . (b) Using Exercise 12,...

Let Xx (1 Let Xk (1 k n) be real valued continuous random variables with joint probability distribution function given by xn) = 91@1) gn(xn where gl, , gn are some functions. Show that Xk (1 k n) are...

please, help me to solve this questions and provide detailed solutions thanks. Problem 3.1 Let x : ($1, . . . ,In) N N(0,In) be a MVN random vector in R". (a) Let U 6 Rnx\" be an orthogonal matrix...

Let (X) be a sequence of independent exponential distributed random variables with means , respectively. log n (a) Does (X) converge in distribution? (b) Does (X) converge almost surely?

Please view attached image for info Problem 3.1 (10 points) Let X and Y be two independent, geometrically distributed random variables with success probability pe (0, 1). Compute the random variable...

The weight, in grams, of the pair of kidneys in adult males between the ages of 40 and 49 has a bell-shaped distribution with a mean of 325 grams and a standard deviation of 30 grams. (a) About 95%...

A firm is considering investing in a project that requires an investment of $40 today. The expected cash flow is $0 for the first year and $50 for the second year. The appropriate discount rate for...

QUESTION 1 ( 3 8 marks ) Food Gallore Ltd ( Food Gallore ) is a large food wholesaler and retailer which sells various food brands. The entity has a 3 0 April financial yearend and is listed on the...

1. A researcher is interested in studying the effects of viewing television violence on aggression in children. She shows one group of participants an extremely violent movie, another group a...

In each of the following data sets, tell whether the outlier seems certain to be due to an error, or whether it could conceivably be correct. a. The length of a rod is measured five times. The...

Following are boxplots comparing the amount of econozole nitrate (in Î¼g/cm2) absorbed into skin for a brand name and a generic antifungal ointment (from the article Improved...

There are 10 employees in a particular division of a company. Their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000. The largest number on the list is...

Observing that HL has a higher ROE, LL's treasurer is thinking of raising the debt-to-capital ratio from 30% to 60%, even though that would increase LL's interest rate on all debt to 15%. Calculate...

Q9. Why should firms that own and operate multiple businesses that have different risk characteristics use business-specific, or divisional costs of capital? a. Not all divisions have equal risk and...

= Sloan Transmissions, Inc., has the following estimates for its new gear assembly project: price = $2,500 per unit; variable costs = $500 per unit; fixed costs = $5.1 million; quantity 80,000 units....