A researcher that wanted to estimate the expectation AY of a random variable Y got three independent observations, Y, Y, Y Theresearcher knows the value o, of the varianceof Y and is considering the following estimators:Pi = 4) Yi + (+) ¥Py = () Yn + (;) ¥½ + () Y½in (}) Yi + (}) ¥z + (()%DWhich of the following is correct?ONone of the aboveOis an unbiased estimator of l and it has the smallest variance of the three estimators.Ois an unbiased estimator of µ and it has the smallest variance of the three estimators.O and i, are both unbiased estimators of fl and Var (ſîz) < Var (îì3).is an unbiased estimator of µ and it has the smallest variance of the three estimators.

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Answered: A researcher that wanted to estimate…

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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Suppose that X and Y are random variables where the conditional expected value of Y given X is given by E (Y|X) = 3X + 6 If X has the expected value 0 and variance Var(X)=9 determine the minimal possible value of the variance Var(Y) of Y./
tion 21. An investor is considering two types of investment. She is quite satisfied that the expected return on investment 1 is higher than the expected return on investment 2. However, she is quite concerned that the risk associated with investment 1 is higher than that of investment 2. To help make her decision, she randomly selects seven monthly returns on investment 1 and ten monthly returns on investment 2. She finds that the sample variances of investments 1 and 2 are 225 and 118, respectively. a) Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2? b) Estimate with 95% confidence the ratio of the two population variances. c) Briefly describe what the interval estimate tells you.
If two independent sufficiently large samples are taken from two populations with known population standard deviations, the sampling distribution of the difference, sample mean (/x)1 - sample mean (/x)2 , between the two sample means /x1 and /x2 a. can be approximated by poisson distribution b. will have a variance of one. c. can be approximated by a normal distribution d. will have a mean of one. I would like to know why the answer is the answer and thank you.
In a psychological testing experiment, 25 subjects are selected randomly and their reaction time, in seconds, to a particular stimulus is measured. Past experience suggests that the variance in reaction times to these types of stimuli is 4 sec2 and that the distribution of reaction times is approximately normal. The average time for the subjects is 6.2 seconds. Give an upper 95% bound for the mean reaction time.
A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Calculator (These samples are chosen independently.) For the people taking Ripped, their sample mean is 9.76 with a sample variance of 11.67. For the people taking Gainz, their sample mean is 7.84 with a sample variance of 1.38. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.10 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? Perform a two-tailed test. Then complete…
Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 12 min and variance 36 min2. (a) What are the values of α and β? α = β = (b) What is the probability that a student uses the terminal for at most 21 min? (Round your answer to three decimal places.)(c) What is the probability that a student spends between 12 and 27 min using the terminal? (Round your answer to three decimal places.)
The critical value for the Pearson's correlation coefficient for two variables collected from 15 people (alpha = 05) would be?
If the X distribution of the number of fines is given by a binomial distribution (x, n = 8, p = 0.7) for values of x = 0, 1, 2,…, 8. a) Find the expected value of X (called the first moment)b) Find the expected value of X2 (called moment second)c) Find the variance of X using the Quick Variance Formula Var (x) = E (X2) - [E (X)] 2d) What will be the expected value of the surcharge R if its function is given by R (X) = X^3 + 50X^2 + 20?
Two airplanes are flying in the same direction in adjacent parallel corridors. At time t = 0, the first airplane is 10 km ahead of the second one. Suppose the speed of the first plane (km/hr) is normally distributed with mean 545 and standard deviation 9 and the second plane's speed is also normally distributed with mean and standard deviation 525 and 9, respectively. (a) What is the probability that after 2 hr of flying, the second plane has not caught up to the first plane? (Round your answer to four decimal places.)(b) Determine the probability that the planes are separated by at most 10 km after 2 hr. (Round your answer to four decimal places.)
Suppose that a random sample of size 20 is taken from a normal distribution with unknown mean and known variance equal to 1, and the mean is found to be i = 10. A normal distribution was used as the prior for the mean, and it was = found that the posterior mean was 15 and the posterior standard deviation was 0.1. What were the mean and standard deviation of the prior?
How did you get the variance for this problem ?

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