Problem 4. Let X1, X2, X3 be a random sample of size n = 3 from a normally distributed randomvariable with mean 2, variance 12. Let Y = X1 - 2X2 +3X3.(a) Find the mean and the variance of Y.(b) Find P(1 < Y < 5).Problem 5. Assume that a quantity is normally distributed with standard deviation 2. A sample of sizen = 30 provides T = 20. Find a 95% confidence interval for the true mean.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Suppose that we have disjoint normal populations A and B with equal population variances. Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance. If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?
An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places
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QUESTION 2 i) If U, and U, each have a normal distribution with mean 0 and variance 20². Furthermore, mu, (t) = etio for i = 1,2. Show that U and U2 are independent.
16. Let X, X2 X, be a random sample from a normal distribution, X, N(6, 25), and denote by X and S2 the sample mean and sample variance. Use tables from Appendix C to find each of the following: (a) P[3 < X < T. (b) P[L860< 3(X-6)/S]. (c) PIS <319375]
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We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?
24. Show that the mean x of a random sample of size n from the distribution : 1 f (x, €) =e, 0 0 x/e e? is the M.L.E. of 0 with variance

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Problem 4. Let X1, X2, X3 be a random sample of size n = 3 from a normally distributed random variable with mean 2, variance 12. Let Y = X1 -2X2 + 3X3. (a) Find the mean and the variance of Y. (b) Find P(1 < Y < 5). A ssume that a guantity is normally distributod wrih