a)Suppose that X₁, X2, X3.....X₂ is a random sample of n from population X which has a chi-square distribution with one degrees of freedom.(i) Find lim Mx (t).1400(ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30.(iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30.

Given Xi~chi square distribution with one degree of freedom, and they are random sample…

Answered: a) Suppose that X₁, X2, X3.....X₁ is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3A) Given P=822-30Q2 and MC=12+9Q find the consumer surplus (CS) (Hint: TR to MR and optimum quantity is MR=MC). B) S=200000 e5find the growth rate of S. C) MC=24eQ and FC=72 Find the total cost. D) The probability of waiting in bus station is given with the frequency distribution f(t)= 1/16 t3 find the probability that your waiting time will be between 1 and 2 minutes?
Suppose X~N(18,25 ) and Y~N(19,16 ). If a sample of size 25 was selected from the X population and another sample, independent of the first, of size 25 was selected from the Y population, then P( X
X = factorial(3) def factorial(n): if n == 1:return 1else:return n* factorial (n-1) def factorial(n):if n== 1: return 1else: 2return n * factorial(n-1) def factorial(n):if n==1: return 1 else:return n* factorial (n-1) Provide a relationship with the domain subset of the integers that is proven using mathematical induction
6
Suppose that the claim size distribution of an insurance portfolio follows a Pareto distribution of the form α+1 α f(x) β = B\B+x (i) Derive a formula for the rth moment, ar, of this Pareto distribution in terms of its (r-1) th moment, αr-1. Show your steps clearly with reasons. (ii) From this expression find α3 and α4 using the known result for the mean μ of the above Pareto distribution. (You may assume that α>r, where a is one of the two parameters of the Pareto distribution).
11 Assume the GPAS of high school students, X, follows a continuous uniform on the domain 1
2.0.3 Problem 3: Central Limit Theorem Here we will verify the Central Limit Theorem and reproduce plots similar to those from Wikipedia (https://en.wikipedia.org/wiki/Central_limit_theorem#/media/File:Dice_sum_central_limit_theorer a) Write a function that returns n integer random numbers, uniformly distributed between 1 and 6, inclusively. This represents n throws of a fair 6-sided die. The value that comes up at each throw will be called the "score". b) Generate a distribution of 1000 dice throws and plot it as a histogram normalized to unit area. Compute the mean ₁ and standard deviation o₁ of this distribution. Compare your numerical result to the analytical calculation. c) Generate 1000 sets of throws of N = 2, 3, 4, 5, 10, 20, 30 dice, computing the total sum of dice scores for each set. For each value of N, plot the distribution of total scores, and compute the mean and standard deviation on of each distribution. This should be similar to the plot at the link above. d) Plot the…
5. Does f(x) = In(x) satisfy the hypotheses of the Mean Value Theorem on [1,4]? If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem.
Solve all plz
7. (12) Show that the hypotheses of the Mean Value theorem are satisfied and find all values satisfying the conclusion for 3 - 7? if r 1
4. Find the value of a so that for f(x) = x³ + ax² - 10x+6 and the interval 0 < x < 4 the location satisfying the Mean Value Theorem is at x = 1.

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