Question: Let (k1, k2, . . . , kt) be the vector of sample observations representing a multinomial random variable with parameters n, p1, p2, .

Let (k1, k2, . . . , kt) be the vector of sample observations representing a multinomial random variable with parameters n, p1, p2, . . ., and pt . Show that the maximum likelihood estimate for pi is ki/n, i = 1, 2, . . . , t.

Step by Step Solution

★★★★★

3.29 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The log of the likelihood vector k 1 k 2 k 4 is log L log p 1 k1 p 2 t2 p 1 k1 k 1 log p 1 k ... 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

Document Format (1 attachment)

681-M-C-M-S (1022).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X be a binomial random variable with parameters n and p. Show that p)n+ n + Dp

If X is a gamma random variable with parameters (n, 1), approximately how large need n be so that 101 01?

If X is a normal random variable with parameters = 10 and 2 = 36, compute (a) P{X > 5}; (b) P{4 16}.

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Project description Type your project, including equations, and submit via Blackboard by 5 pm on May 26. The recommended program for doing this is LaTeX (see http: //www.latex-project.org/) together...

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

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...

The best definition for nonparametric statistics I can think of is when data does not fit inside the normal parameters of a normal distribution, it calls for the use of this statistical method....

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

Fluctuation in the target interest rate in the New Keynesian model lead to all of the following except A. procyclical real wages. B. procyclical employment. C. countercylical prices. D. procyclical...

The following table shows a sample of property listings and values from one neighborhood (one ZIP code) in the Washington, DC, area in December 2011: a) In this sample, what proportion of homes is...

2.43 The figure for this exercise is a histogram summarizing the responses given by 116 college students to a question asking how much they had slept the previous night (Data source: sleepstudy...

Discuss the Box-Pierce Q-test statistic and Ljung-Box Q test for testing the higher-order autocorrelation problem.

Continuation of Exercise 4-140. A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal in order for...

Continuation of Exercise 140 Rework parts (a) and (b). Assume that the lifetime is an exponential random variable with the same mean.

Continuation of Exercise 4-140. Rework parts (a) And (b). Assume that the lifetime is a lognormal random variable with the same mean and standard deviation.

Zambezi Corp. expects EBIT to vary with the state of the economy as follows: 560 State of economy EBIT in $ million) Boom Base 125 Bust -200 Zambezi doesn't have any long-term debt and has 95 million...

Case 1 Case 2 Case 3 Direct material used 20,000 12,300 Direct labor 11,000 Manufacturing overhead applied 12,000 Total current manufacturing costs 29,000 28,500 Beginning work in process inventory...

Today you go long on 4 December contracts of lean hog futures, at a price of 6 6 . 6 cents per pound. One contract is for 4 0 K pounds. One month later, December futures are trading at 5 6 . 7 cents...