b) Let Z₁ =*-~N(0,1), and W₁=~N(0,1), for i=1,2,3,...,10, then:i) State, with parameter(s), the probability distribution of the statistic, T = -10ii) Find the mean and variance of the statistic T =iii) Calculate the probability that a statistic T = Z₁Σας Ζα+ W₁ is at most 4.

Given Zi~N(0,1) and Wi~N(0,1) Result: t~F(a,b) Then Mean=E(t)=b/(b-2)…

Answered: b) Let Z₁ =*#*~N(0,1), and W₁ =~N(0,1),…

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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B4
Q1) 14% of the adults in a certain population are infected by a Corona Virus. Five adults are selected randomly from this population for diagnoses. Find the probability that at least two of them will be infected by .this Virus 1 .Q2) Suppose that f(X)=X,12). a) Find .b) Find the mean Q3) A study shows that the systolic blood pressures for adults in a certain population are approximately normally distributed with mean of 115 and .standard deviation of 10 a) Find the probability that a randomly selected person will have a blood -pressure between 109 and 124 Sel).b) Find the reading that is exceeded by only 5% of the population التي يتجاوزها 5% من المجتمع(
A.2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter lambda. a) If X1, X2. ..., Xp are the times, in minutes, between Successive customers selected randomly, estimate the parameter of the distribution. b) The randomly selected 15 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, 1.8, 0.9, 1.5 and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.4 error and 4% risk, find the minimum sample size.
a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04? QUESTION A
36) The time X needed to complete a final examination in a particular College Course is normally distributed with a mean of 60 minutes and standard deviatation of 10 minutes. The Probability of completing The exam in less than 70 minutes. is A) 0.9655. B)0, 1387 C) 0.8413 D) 0.0345
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Find conditional probability Find mean and standard deviation 11)The age of customers at a local hardware store follows a uniform distribution over the interval from18 to 60 years old. Find the average age of customers to this hardware store. 140). 12) Suppose x is a uniform random variable with a = 20 and b = 80. Find the standard deviation of x. Find mean and standard deviation
Suppose X1, X2, ... , Xn is a random sample and Xi = {1, with probability p 0, with probability 1-p} for every i = 1, 2, ... , n. Find the Moment Generating Function of ∑i=1n Xi . What is the distribution of ∑i=1n Xi ?
23
5. Let (*1, x2, .., rn) be n independent random sample of size n from a uniform distribution on the interval [01,02]; (a) find the c.d.f of, X(1), the minimum order statistic (b) find the c.d.f of, X(n), the maximum order statistic (c) Hence, find the mean and variance of X(1) and X(n)-
c) Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X? 2| Page

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