Suppose the random variable, X, follows a Bernoulli distribution with parameter 0.The probability function of X is given byp(x; 0) =0² (1-0)¹-² if x = 0, 1,otherwise.0Let X₁, X2,, X₁ be a random sample of size n from the population of X. Assumethat the X's are independent and identically distributed with the same parameter.(a) Based on the joint probability function of the sample, state the likelihoodfunction of the parameter. Discuss the difference between the joint probabilityfunction and the likelihood function.(b) Show that the sample mean is the maximum likelihood estimator (mle) of 0.(c) Find the method of moments estimator (mme) of 0.

Answered: Image /qna-images/answer/bb54c1b6-0780-4015-a9d5-af4311d181b5.jpg

Answered: Suppose the random variable, X, follows…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

b) Suppose that a continuous random variable X is associated with the following function: (i) Show that c = =1/15 2 71 Page 0 < x < 2, Scx, f(x) = {0, elsewhere. lo, (ii) Calculate the mean and variance of X. (iii) Find the CDF of the random variable X, F(x). (iv) Use either the probability distribution function (pdf) of X, f(x), or the cumulative probab distribution function (cdf) of X, F(x), to compute P(0.25 < x < 1.25).
Suppose X and Y are two random variables with E[X] = 1, Var (X) = 4, E[Y ] = -1, Var (Y) 4, and Cov (X, Y) = 1. Find the standard deviation of (X - Y). = (a) 2 (b) √2 (c) 6 (d) √6 (e) None of the above
Let X and Y be independent exponential random variables with parameter 1. Find the cumulativedistribution function of Z = X/(X + Y )
Let X1, X2,.., X, be independent identically distributed random variables with each X, having a probability mas function given byP(X; = 0) = 1-p P(X; = 1) = p, where Osps1. 1 EXj, then E(Y)= j = 1 Define the random variable Y = n Select one: а. 1 b. p C. 0 d.
If the joint probability distribution of X and Y isgiven byf(x, y) = 130 (x + y) for x = 0, 1, 2, 3; y = 0, 1, 2 construct a table showing the values of the joint distribu-tion function of the two random variables at the 12 points (0, 0),(0, 1), ... ,(3, 2).
1
9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)
Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)
B) Let X1,X2, .,Xn be a random sample from a N(u, o2) population with both parameters unknown. Consider the two estimators S2 and ô? for o? where S2 is the sample variance, i.e. s2 =E,(X, – X)² and ở² = 'E".,(X1 – X)². [X = =E-, X, is the sample mean]. %3D n-1 Li%3D1 [Hint: a2 (п-1)52 -~x~-1 which has mean (n-1) and variance 2(n-1)] i) Show that S2 is unbiased for o2. Find variance of S2. ii) Find the bias of 62 and the variance of ô2. iii) Show that Mean Square Error (MSE) of ô2 is smaller than MSE of S?. iv) Show that both S2 and ô? are consistent estimators for o?.
If pdf of a random variable is given by fx(x) = e* for x20 find My(v), m, and m,. X

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS