Let Y₁, Y2, ..., Yn be a random sample from a population that is uniformly distributed on theinterval (0,50).Note that both the lower and upper bounds of this interval depend on a single unknown parameter 0.Let AY be an estimator of 0. (Consider the sample mean as a candidate estimator for theparameter.)Compute the mean squared error of the estimator Î.=

Answered: Let Y₁, Y2, ..., Yn be a random sample…

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 maximum patent life for a drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below, where Y is a random variable representing actual patent life of a drug (in years): y P(Y=y) F(y) 4 5 6 7 8 9 10 11 0.06 0.08 0.11 0.15 0.22 0.18 0.12 0.08 a) Complete the table above with the cumulative probability distribution for actual patent life (F(y) = P(Y ≤ y)). b) What is the probability that the actual patent life of a random drug is 6 years or less? c) What is the probability that the actual patent life of a random drug is more than 8 years? Show this in two ways: i. using the probability distribution for Y ii. using the cumulative probability distribution for Y, and applying our probability of comple-…
A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for of
Suppose that X₁,..., Xn are i.i.d. from a normal population with mean μ and variance o². Calculate the expected value and the variance of the sample mean X and find the distribution of √n(X − µ).
If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? Explain
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let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).
The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?
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