1. Consider a random sample of size n from a distribution with CDF F(x) = 1 1/x if1 18. In Exercise 1, find the limiting distribution of n In X1:0.

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Answered: 1. Consider a random sample of size n…

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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Determine the cumulative distribution function for the random variable Xwith the probability mass function fx) = (3/4)(1/4)*. The range of Xis {0, 1, 2, ...}. Give non-integer answers in the form of proper fractions for the cumulative distribution function values listed below. F(0) = F(1) = F(2) = F( + 0) = i
X = the number of occurrences of a particular event in an interval of time or space. 2x. e-2 P(X = x) = X = 0, 1, 2, 3, .... %3D х! Е(X) - 7, Var(X) = .. Table III (pp. 580 – 582) gives P(X< x) 1. Traffic accidents at a particular intersection follow Poisson distribution with an average rate of 1.4 per week. a) What is the probability that the next week is accident-free? b) What is the probability that there will be exactly 3 accidents next week? c) What is the probability that there will be at most 2 accidents next week?
3. Draw the cumulative distribution functions of the following distributions: (a) A continuous random variable chosen uniformly from the interval [1,6]. (b) A continuous random variable chosen uniformly from the union [1,2] U [3, 4] U [5, 6]. (c) A discrete random variable chosen uniformly from the set {1, 2, 3, 4, 5, 6}.
(a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of X = (ii) If 1 = 0, name the distribution of X given in 3(a)(i).
iid X1,..., Xn Geo(p) where 0 0; B>0]a conjugate family for samples from the Geometric distributions [Geo(p): 0 0 are known constants. C- Derive the Bayes estimator of p. d- Express the estimator in part (c) as a weighted average of the prior mean of p and the MLE of p.
A random variable has poisson distribution such that P (X = 3) = P (X= 4). Find p (6).
Assume that X is a random variable whose conditional distribution given the variable Y is poisson P (X | Y) = Po (Y). Suppose further that Y has a gamma distribution Y ∼ Gamma (1, 1). (a) Determine the value E (XY). (b) Determine the conditional distribution P (Y | X).
Let {N(t); t ≥ 0} be a renewal process with the gamma distributed inter- occurrence times with parameters 2 and 3 .The probability distribution of waiting time until the fifteenth renewal occurs is Select one: a normal distribution with paramters 10 and variance 3.33 O b. normal distribution with mean10 and variance 50 gamma distribution with parameters 30 and 3 O d. gamma distribution with parameters 30 and 45 O C.
1. A discrete random variable X follows the Uniform distribution if X takes values x = 1, 2, .., N, with P(X = x) = 1/N. Compute E(X), E(X²) and the variance Var(X). You may use the following identities: п(п + 1) (1) 2 п(п + 1)(2n + 1) (2) i=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}.)
What is the theoretical expectation for the population space? Variance? and Standard Deviation?

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1. Consider a random sample of size n from a distribution with CDF F(x) = 1 − 1/x if 1