Suppose X,n} is a sequence of random variables draw from an underlying popu-lation space, then the sample mean of {Xn} defined as Xnin distribution to Normal Distribution N(u, a2), where u E[X3], o2:E1Xi, convergeVar[X Plot the histogram of 2000 sample mean X10 together with N(20, 2). Whatis your conclusion from the graph.

From the given information, the sample mean X10-bar follows normal distribution N(20, 25/10).That…

Answered: Suppose X,n} is a sequence of random…

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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According to a study, the length of pregnancy has an unknown distribution with a mean of 265 days and a standard deviation of 15.4 days. Let XX be the length of pregnancy for a randomly selected female and let ¯¯¯XX¯ be the average length of pregnancy for a random sample of size 22. 1. Describe the probability distribution of XX and state its parameters μμ and σσ: X∼X∼ ( μ=μ= , σ=σ= ) 2. Explain why the Central Limit Theorem can or can not be applied The Central Limit Theorem for Sample Means be applied because
Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?
Suppose that X1,X2,...,X200 is a set of independent and identically distributed Gamma random variables with parameters α = 4,λ = 3. Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.
Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes (uniform distribution). Letting the time unit be one minute, Find the probability that a randomly selected flight between the two cities will be at least five minutes late (greater than 2 hours 15 minutes). What is the probability the plane will arrive plus or minus 1 standard deviation away from the mean? (Hint: Calculate the mean and standard deviation. Add the standard deviation to the mean to get plus 1 standard deviation away from the mean and subtract the standard deviation from the mean to get minus 1 standard deviation from the mean. Then use these two numbers as your a and b),
Suppose the traffic light at a specific intersection changes to green at 4-minute intervals. If a car arrives at the traffic light at a random time, then X = waiting time in minutes, is uniformly distributed between 0 and 4. Suppose a random sample of 35 cars are observed and their waiting time is recorded. What is the probability that the sample mean of the waiting times is less than 1.5 minutes?
A computer of random numbers with a uniform distribution between 0 and 1 manufactures. A standard deviation of 1 by adding the n random numbers generated. Normal distribution is desired. Where the found n is large enough assuming that the new random variable generated from the sum of these n random numbers what is the average?
The weight of breads prepared in a baker is randomly distributed with a mean of 400 grams and standarddeviation of 16 grams. Using an independently selected sample of 16 breads,finda) the mean and standard deviation of the average weight of these 16 samples.b) using central limit theorem, estimate the probability that the average weight of samples is less than390.
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 5 minutes. Find the probability that a randomly selected passenger has a waiting time less than 0.75 minutes.
The central limit theorem describes three important properties of all distributions of sample means of any given sample size. What are the three properties it describes?
Suppose that an airline quotes a flight time of 2 hours 10 minutes between two cities. Furthermore, suppose that historically flight records indicate that the actual flight time between the two cities, X, is uniformly distributed between 2 hours and 2 hours 20 minutes. Expressing time in minutes: a) Discuss the probability curve of X. b) Find the probability that a randomly selected flight between the two cities will be at least five minutes late. c) Calculate the mean flight time and the standard deviation of the flight time.
The proportion of individuals that regularly smoke in a population is known to be 0.25. Applying the results from central limit theorem, What is the probability that a random sample of 1000 individuals drawn from the population will have atleast 260 smokers?
A radioactive source is observed during 7 time intervals each of ten seconds in duration. The number of particles emitted during each period is counted. Suppose that the number of particles emitted, say X, during each observed period has a Poisson distribution with parameter 5.0.(That is, particles are emitted at the rate of 0.5 particles per second.)(a) What is the probability that in each of the 7 time intervals, 4 or more particles are emitted?(b) What is the probability that in at least 1 of the 7 time intervals, 4 or more particles areemitted?

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