Answered: Consider a Poisson distribution with…

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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The population of college students using “normal shoes” is able to complete a particular racecourse in an average of 250 seconds. The standard deviation for this population is 20 seconds and the population is normally distributed. A random sample of 28 college students is given a special pair of new shoes and asked to run the course. The average “race time” for this group is 243 seconds. assume now that the designer of the shoes states that his shoes should improve the times of the user (less time to finish the race). State the hypotheses involved. determine if the hypothesis test is one tailed or two tailed Give the Z scores associated with cut-off points for .01, .05, and .10 (1%, 5%, and 10% respectively). Calculate the Z score for this problem. Based on a cut-off point or alpha level of .05 (5%), what decision would you make about your hypotheses? Explain this decision. Make conclusions regarding the specifics of this study.
Suppose that X~N(5000,400). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 5000. If you took a sample of size n = 100, what is the standard deviation of that sample?
The number of babies in a litter of rabbits is approximately Poisson distribution with mean 6. Litters can occur once per month for a 9 month period (3 months infertile). What is the standard deviation of the number of babies in one litter? What is the probability of a litter with exactly one rabbit? What is the approximate probability that over a 9 month period, a rabbit will have more than 65 babies (use the Central Limit Theorem, continuity correction is optional)? Incidentally, the plot at right shows the exact Poissondistribution you’ll be using, and you’ll note it looks quite a bit like some other distribution . .
I want to ask how do we know when we need to use the continuity correction like the second image and when will we use the normal distribution like the 1st image? Thank you
Suppose the random variable X has a continuous uniform distribution on the interval (20,80). What is P(X > 52 | X > 28)? (Give your response to at least 3 decimal places
The random variable x is known to be uniformly distributed between 10 and 15 . 1. Compute P(x < 13.5) (to 2 decimals)
please help me solve both parts a and b. please do not round your answers. if you solve correctly i will be glad to rate you. thank you so much for your help.
Suppose that X~N(5000,400). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 5000. If you took a sample of size n = 10000, what is the standard deviation of that sample?
Suppose that X~N(500,100). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 500. What is its standard deviation, if you took a sample of size n = 10000?
Q1: Suppose the number of customers X that enter a store between the hours 9:00 a.m. and 10:00 a.m. follows a Poisson distribution with parameter 0. Suppose a random sample of the number of customers that enter the store between 9:00 a.m. and 10:00 a.m. for 10 days results in the values 9, 7, 9, 15, 10, 13, 11, 7, 2, 12 Determine the maximum likelihood estimate of 0. Show that it is an unbiased estimator. Q2: Assume that X is a discrete random variable with pmf f(x). Let X₁,...,X₁ be a random sample on X. Suppose that the space of X is finite, say, D={a₁,...,m}. An intuitive estimate of p(a) is the relative frequency of a, in the sample. We express this more formally as follows. For j=1, 2,..., m, define the statistics 1,(X) = {1 0 X₁ = a; X₁ = a; Then the intuitive estimate of p(a)) can be expressed by the sample average p(a) = -1,(X₂) Find the unbiased estimator and the variance of the estimator and its mgf.

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Consider a Poisson distribution with = 4.6 Compute f(x greater than or equal to 3) (ANSWER MUST BE 4 DIGITS)