Let Y be a random variable with an exponential distribution with E(Y) = 0, and supposed a single observation of Y wastaken from the population.a) Show that the pivotal2Yhas a chi-square distribution using the moment generating function technique. What are thedegrees of freedom for this distribution?b) Using the pivotal quantityderive a 95% confidence interval for 0.c) Imagine an observation of Y = 1.5 was collected, compute the 95% confidence interval. Does this interval contain thepopulation parameter? Explain your answer.

From the given information, Y be a random variable with an exponential distribution with E(Y)=θ.…

Answered: Let Y be a random variable with an…

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 number of people who dine at restaurants in Buffalo is normally distributed with a µ = 30 people and = 3 people. (Report both the z-scores and probability) What is the probability that the mean of 7 restaurants will have between 21 and 32 people dining there? z1 = z2 = p(21 > M > 32) = What is the probability that the mean of 13 restaurants will have less than 21 people dining there? z = p(M < 21)= Is the p=0 when the z score is extreme like -10 or 10?
6??
part iii (i already asked part i and part ii)
Suppose a simple random sample of size n=10 is obtained from a population with μ=68 and σ=19. Answer a-c (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x<71.1). (c) Assuming the normal model can be used, determine P(x≥69.2).
d,e,f e) This result would be (usual, unusual) so the sample likely came from a population whose mean gestation period is(less, more, equal) to 266 days
Let X is a random variable with a pdf with mean u and standard deviation o (we do not know the actual shape of the pdf). If we draw reasonably large (n) samples from X, and calculate the sample mean X-bar, then what will be the pdf of the X-bar and WHY? |(Do not forget to mention the parameters of the pdf of X-bar) Answer here--->
SAT scores in one state is normally distributed with a mean of 1496 and a standard deviation of 64. Suppose we randomly pick 43 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1503. P(X > 1503) = b) Find the probability that the average of the scores for the sample of 43 scores is greater than 1503. P(X > 1503) = Round each answer to at least 4 decimal places.
The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 18. Suppose that 48 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. For the 48 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 66.6 and 69.5. For part d), is the assumption that the distribution is normal necessary? Yes or No

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