Question: 4. Let X1, X2, X, denote a random sample from the Log-Normal distribution with probability density function (pdf) 1 f(x; ) = exp X2

4. Let X1, X2, X, denote a random sample from the Log-Normal

4. Let X1, X2, X, denote a random sample from the Log-Normal distribution with probability density function (pdf) 1 f(x; ) = exp X2 {- (In x-u)2 x>0 2 4.1. Show that the log-normal distribution is a member of the exponential family of distributions and give T(X) the complete sufficient statistic for u. [5]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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!

Consider the following set of ordered pairs: Assuming that the regression equation is y = 1.886 + 0.977x and that the SSE = 0.7955, test to determine if the slope is not equal to zero using = 0.05....

ways to write a short case study about one business (NOT brand or Group) in one of the following hospitality sectors such as food sector. how to evaluate the business in real world by including...

Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...

Question 1 Let X1, X2, .., Xn be a random sample drawn from a distribution with probability density function f (x; 0) = 7 ( 1 + x ) 0+ 1, 0 0 is an unknown parameter. (a) Show that Y, = In(1 + X;)...

Let X1, X2, ... Xn be a random sample drawn from a distribution with probability density function f (x; 0) = (1 + x)0+1, 0 0 is an unknown parameter. (a) Show that Y, = In(1 + X;) follows a Gamma (a,...

Answer all the questions 2. Let X - {X1, X2. . . ., X} be a random sample drawn from the distribution with probability density function: fx (1: 0) = otherwise. (a) Derive the probability density...

{a} Consider testing the hypotheses Hg versus H1 at the 0.135 level of signicance using one ohseivation .v (n = 1). (1') Determine the critical value, c' of the test that rejects Ha if Iv 1.11.3.3 _"...

QUESTION 1 A distribution belongs to the regular 1-parameter exponential family if among other regularity conditions its pd f or pmf has the form: Question 1 A distribution belongs to the regular...

Please input every question into R. thank you! 2. (a) Consider random variable X1, X2,..., X,. from a Poisson distribution with 2 = 2. State the probability density function (pdf) and its...

4. Match each description to the term to which it applies most. Term Description ________ Program management a. Establishes an organizations purpose, vision, and goals, and how to achieve them...

Epsilon inc. has just paid a dividend of $3 per share, and it is expected to pay a dividend of $3.15 per share in one year's time. Assuming that required return is 13% and the dividend growth will...

FAR 9.104-5 certification regarding responsibility matters is a DOD federal Acquisition Regulation that addresses the purchasing and disposition of items that are nonconforming. Explain.

Apply SAS 99 (AU-C 240) and identify red flags (fraud risk factors) that are present in the Moha case. Red flags should be grouped under three categories: pressures/incentives, opportunities, and...

In problem use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y" + 9y = cos 3t, y(0) = 2, y'(0) = 5 Appendix III = F(s)...

The 0.4-lb ball and its supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angular velocity of 4 rad /sec. The ball is held in the position b = 14 in....

A tank of water (15C) with a total weight of 200 N (water plus the container) is suspended by a vertical cable. Pressurized air drives a water jet (d = 12 mm) out the bottom of the tank such that the...

A particle moves along the curved path shown. The particle has a speed v A = 12 ft/sec at time t A and a speed v B = 14 ft/sec at time t B . Determine the average values of the normal and tangential...

can you break down the 4 villains and explain what the mean villain 1 Any time in life you're tempted to think, 'Should I do this OR that?' Villian 2 The "confirmation bias, villain 3 "Short-term...

The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables: a. T = the total number of pumps...

An experiment was carried out to compare flow rates for four different types of nozzle. a. Sample sizes were 5, 6, 7, and 6, respectively, and calculations gave f = 3.68. State and test the relevant...

Consider a normal population distribution with the value of known. a. What is the confidence level for the interval 2.81 /n? b. What is the confidence level for the interval 1.44 /n? c. What...

=+b. Suppose the investigators had believed a priori that the population standard deviation was about 4 MPa. Based on this supposition, how large a sample would have been required to estimate to...

=+26. Researchers have developed a chemical treatment that retards the growth of trees of a certain type whose branches pose a safety threat to power lines. However, an overly severe application of...

=+a. Calculate a lower confidence bound at the 95% confidence level for the true proportion of such hips that develop squeaking.