(25) Consider a population {1,2,3} which has only three numbers. (5) What are the relationships of...

(25) Consider a population {1,2,3} which has only three numbers. (5) What are the relationships of the individuals of a random sample, namely X_1,X_2…,X_n (5) If we sample with replacement from this population with sample size =2, what is the distribution of sample mean (Distribution table)? (5) If we sample without replacement from this population with sample size=2, what is the distribution of the sample mean (Distribution table)? (10) If we sample with replacement from this population with sample size=100, state the theorem for finding the distribution of the sample mean. What is the distribution of the sample mean (including the mean and variance)?

Expert Solution

(a) Each individual has probability of being selected in the random sample with discrete uniform distribution in the set of values={1,2,3}

(b)

(c)

(d)

orchestra answered 1 year ago

Consider a toy population that consists of three numbers 1,2, and 3. A. Let X be...

Consider a toy population that consists of three numbers 1,2, and 3. A. Let X be the randomly selected number (P(X = x) = 1/3) for x = 1,2,3. Find E(X) and V(X). B. What are the values of the population mean µ and population variance σ^2? C. Take a random sample of size n = 2 (with replacement). Determine the sampling distribution of the sample mean x̄, i.e. find the probability for each possible value of x̄. D. Find...

A particular mattress company has three factories (1,2,3), each of which produces three types of mattresses:...

A particular mattress company has three factories (1,2,3), each of which produces three types of mattresses: (1) spring, (2) foam, and (3) hybrid. In the matrix ? = [ 80 50 25 45 110 60] ??? represents the number of mattresses of type ? produced at factory ? in one day. Find the production levels if production increases by 15%.

5. Using only the digits of 1, 4, 5, 8, (a) How many three digit numbers...

5. Using only the digits of 1, 4, 5, 8, (a) How many three digit numbers can be formed? (b) How many odd numbers greater than 10 can be formed? (c) How many even number less than 300 can be formed? Repetition is allowed!

Six different numbers are chosen at random from the set {1,2,3, … ,50}. a) What is...

Six different numbers are chosen at random from the set {1,2,3, … ,50}. a) What is the probability that a number greater than 40 is selected? b) What is the probability that a number greater than 40 is selected and a number less than 10 is selected?

Consider a random sequence x1,…,x7 of 7 numbers each chosen from the set {1,2,3,…,10} with replacement....

Consider a random sequence x1,…,x7 of 7 numbers each chosen from the set {1,2,3,…,10} with replacement. What is the probability that max{x1,…,x7} occurs exactly once in x1,…,x7?

Consider the set of real numbers S=[-1,0)U{1/n:n=1,2,3,...}. Give the explicit set for each of the The...

Consider the set of real numbers S=[-1,0)U{1/n:n=1,2,3,...}. Give the explicit set for each of the The complement of S, The closure of S, The boundary points of S, The limit points of S, The isolated points of S, The interior of S, and The exterior of S.

Consider the function ?(?)=(?^(4/5))*(?−3). This function has two critical numbers ?<? 1) Then ?= ? and...

Consider the function ?(?)=(?^(4/5))*(?−3). This function has two critical numbers ?<? 1) Then ?= ? and ? = ?. 2) For each of the following intervals, tell whether ?(?) is increasing or decreasing. (−∞,?]: ? [?,?]: ? [?,∞): ? 3) The critical number A is ? and the critical number B is ? (a relative maximum / a relative minimum / neither max nor min ) There are two numbers ?<? where either ?″(?)=0 or f″(x) is undefined. 4) Then C...

SumOfTwoHighest returns the sum of the two largest numbers SumOfTwoHighest(1,2,3) ➔ 5 SumOfTwoHighest(0,1,0) ➔ 1 SumOfTwoHighest(-1,-2,-3)...

SumOfTwoHighest returns the sum of the two largest numbers SumOfTwoHighest(1,2,3) ➔ 5 SumOfTwoHighest(0,1,0) ➔ 1 SumOfTwoHighest(-1,-2,-3) ➔ -5 int SumOfTwoHighest(int i, int j, int k) { } #include <iostream> using namespace std; int SumOf3Digits(double d) { string s = to_string(d); int sum=0; for(int i=0;i<s.size();i++) { if(s[i]!='.')sum= sum+ s[i]-'0'; } return sum; } int max(int i, int j) { return i>j? i:j; } int Power(double d, int pow = 2) { if(pow == 0) return 1; if(pow == 1) return d;...

Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose...

Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose product is 64 and whose sum is minimal is give by {4, 4, 4}. (a) When is an absolute minimum or maximum guaranteed? (b) State the steps to find an absolute minimum and maximum. (c) Is the space closed and bounded? Explain. (d) Use Lagrange Multipliers to find the minimum and maximum please label and write neatly.

QUESTION 1 (25 MARKS) a. Given a population has a mean of 125. What is...

QUESTION 1 a. Given a population has a mean of 125. What is the sampling error for an eight items sample with the values 103, 123, 99, 107, 121, 100, 100 and 99? b. United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems. United supplies these valves to major companies such as Rain Bird and Nelson, who in turn sell sprinkler products to retailers. United recently entered into a contract to supply 40,000...

Question