a)b)Suppose that X₁, X₂, X3.....X is a random sample of n from population X which has a chi-square distribution with one degrees of freedom.(i) Find lim Mg(t).(ii) Use the Central Limit Theorem to compute P(0.5 <<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.Let X₁, X₂, X₁X be a random sample of n from population X distributed with the followingprobability density function:f(x:0)=√200,if -∞

Given that X1,X2,.....,Xn is random sample of "n" from the population X Xi follows Chi-square…

Answered: Suppose that X₁, X₂, X3 X is a random…

A First Course in Probability (10th Edition)

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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...

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Suppose Xn is the sample mean of a random sample of size n from a distribution that has a Gamma(2,1/2) (where a = 2, B = }) pdf f(x) = 4xe-2a, 0 < x < ∞, zero elsewhere. Use the Central Limit Theorem to deduce that the random variables Vn(Xn – 1) converges in distribution to N(0, 1/2).
(i) Let X ~ Poisson(A). Then, using Chebyshev's inequality, show that P(X > 21) < 1/A. (ii) Suppose that the number of errors per computer program has a Pois- son distribution with mean 5. We get 125 programs. Let X1, X2, ..., X125 be the number of errors in the programs. Then, using the central limit theorem, find an approximate value for P(Xn < 5.5).
(c) What is the asymptotic distribution of √n(0-0)? 6.2.9. If X1, X2,..., Xn is a random sample from a distribution with pdf ={ f(x; 0) = 303 (x+0)4 0 0
An actuary models loss amounts under a insurance policy using the Pareto distribu- tion. The cdf of the Pareto distribution Suppose that 0 = 1400 and a = 1.6. What is the expected is F(x) = 1 (0/(x+0))ª. payment under a claim given that the policy has a deductible of 350 and a limit of 1300?
The following table shows the price per share of Apple stock at the beginning of different months. Calculate the four-month weighted moving average for October 2021. Round your answer to the nearest cent. Month July 2021 August 2021 September 2021 October 2021 November 2021 December 2021 Apple Stock Price Simple Moving Average Weighted Moving Average $136.60 $146.36 $152.83 $141.90 $148.99 $167.48 ???
a) Suppose that X₁, X₂, X3,...,X, is a random sample of n from population X which has a c square distribution with one degrees of freedom. (1) Find lim Mg(t). 72-00
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).
Please show as many steps as you can so i can understand the proccess.
20. Let X1, X2, ables, and set X, be independent, Exp(a)-distributed random vari- Y1 = X(1) and Y = X(k) – X(k-1); for 2
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Given that Z - N(O, 1) use tables to evaluate correct to three decimal places then P(1.24 < Z < 2.36)=
7.

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