STAT 311: Mathematical Statistics Homework 02 Chapter 5: Point Estimation 1- Let X, ,...,X, be a random sample of size n from the geometric distribution for which p is the probability of success. (a) Use the method of moments to find a point estimator for p. (b) Use the following data (simulated from geometric distribution) to find the moment estimator for p: 5 43 18 19 16 11 22 4 34 19 21 23 6. 21 12 2- The probability density of a one-parameter Weibull distribution is given by S2ax e¬ax² 0, x > 0 otherwise f(x) = - (a) Using a random sample of size n, obtain a moment estimator for a. (b) Assuming that the following data are from a one-parameter Weibull population, 1.87 1.60 2.36 1.12 0.15 1.83 0.64 1.53 0.73 2.26 3- Suppose X, ,...,X, are a random sample from an exponential distribution with parameter 0. Find the MLE of Ô. Also using the invariance property, obtain an MLE for the variance. 4- Let X1 .,X, be a random sample from a two-parameter Weibull distribution with pdf .... xa-1e(x/ß)“, x >0 f(x) 0, otherwise Find the MLES of a and ß. 5- Consider the problem of estimating p in a binomial distribution. Let X be number of successes in a sample of size n. (a) Let the prior distribution of p be given by Beta(3,1), that is T(p) = {3p², 0

Q: 9. If we were to repeat the process in # 1 -6 for n=3 dice, there would be 216 possible outcomes…

A: Given: n=3 dice μX¯=3.5 σX¯=1.713

Q: Question 2 of 25 : Select the best answer for the question. 2. What is $3,850 minus $925 ? A. $925…

A:

Q: the true answer is $

A:

Q: and question d

A: As per the  question we have to find the constant force of interest that will give rise to the…

Q: Find all real numbers k such that the system of linear equations has infinitely many solutions.…

A:

Q: Need questions 4 5 and 6 answered please

A: 4. Given: μ=70, σ=5 The corresponding z-values needed to be computed: The probability that a score…

Q: parts iv and v please

A: Given is a question on the probability of failure/success. Number of failed O-rings 0 1 2 3 4 5 6…

Q: Need help for question 1. And question 2.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: im 2. 3. 2.

A:

Q: Listed below are recorded speeds (in miles/hour: mph) of randomly selected cars traveling on a…

A: Given that midpoint of first class is 56 and class width is 3. Arrange the data in ascending order…

Q: Match the following graph to its inverse. -5-4-3-2 5 3 ↑ M T + 1 2 3 4 5

A:

Q: Question 9 da =

A: Our Aim is to integrate the Integral given below:-∫14x2xdx  -(i)

Q: Question 1 Assume that the following relationship is known to be true for two angles A and B: sin A…

A: SinA cosB - cosA sinB = 0.981663  Express A in terms of B.  We know the identity  SinA cosB - cosA…

Q: . 4- 5 4m+8

A:

Q: 1 Evaluate. 5P3 • 6C4 900 300 150

A: Use the formula and evaluate.

Q: the

A:

Q: 11C6

A: we know that,Cr=n!(n-r)!×r!nand r!=r(r-1)(r-2).....×2×1

Q: answer question 4.

A:

Q: 1. Simplify. (6-2)³ - (5 +5²) O-14 -32 34 5

A: The given expression        6-23-5+52

Q: Perform the indicated operations.   having trouble with these types of questions.

A:

Q: More answers for that question pl

A: Solution: Given information: Test statistic χ2=23.75 P value = 0.0006

Q: Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land…

A: Hello there! there are more than three sub parts in the question. according to our policies cannot…

Q: Questions c-e

A: First find out the measures of center i.e. mean , median & mode .  The mean of a data set is the…

Q: 11V-6 11V2

A: We have given  11√-6/11√2

Q: what about questions 4-15?

A:

Q: Simplify. 1 -2 - 5 +y -1 -2 + y X

A: Topic- Equation

Q: Given below are the weekly donations at a local charity for the last five weeks. week 1 3. amount…

A: The four week moving average forecast for week 6 is obtained by taking the average of week 2 to week…

Q: BCD???

A: Given problems:- b) ∫6w3+7wdwc) ∫y+14ydy d)∫123z-24dz

Q: Question 12 32K

A:

Q: Questions 1, 2, and 3

A: Given, The figure shows the point estimates for the population mean concentration and the 95%…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.