Problem 3: Suppose X is a discrete random variable that takes on integer values between 1 and 10, withvariance Var(X) = 6. Suppose that you define a new random variable Y by observing the output of X andadding 3 to that number. What is the variance of Y? Suppose then you define a new random variable Z byobserving the output of X and multiplying that by -4. What is the variance of Z?

Introduction: Suppose X is a random variable with standard deviation, σ, that is, variance σ2.…

Answered: Problem 3: Suppose X is a discrete…

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 you would like to keep a test tube at 48F (exactly), but your refrigeration unit exhibits some random fluctuations, so that the difference between the temperature at which you set the thermostat and the true temperature is distributed normally with mean 0 and variance 1.96. What is the highest you can set the thermostat and be 95% sure that the true temperature is no more than 48F?
Suppose that we have disjoint normal populations A and B with unknown population variances. Suppose we have a sample of size 1O from from population A and a sample of size 15 from population B which we would like to pool to form the pooled variance. But, for this we need to assume that the population variances are equal. If the sample variance for the sample from population A is 11 and the sample variance for the sample from population B is 7, then does our data actually give evidence that the two population variances are actually different? Give the P-Value of this data as evidence that the two population variances are different (use stattrek.org). .44 1.56 .22 .78 NONE OF THE OTHERS
A nail is needed to hang up a 50 lb painting on a wall. A technician has two nails in his pocket, where the probability that both nails meet the specific weight of the painting is 50%, the probability that only one of them meets the specific weight is 20%, and the probability that neither of them meets the specific weight is 30%. If the number of nails that meet the specification is a random variable, find the variance of the data of that random variable.
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?
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: �"!= 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4.What is the variance of � "!
During a month in Adana, it rains with probability 2/3 each day, independently of every other day. Compute the variance of the number of rainy days in this month (a month=30 days). а. 1 O b. 1/3 O c. 2/3 O d. 20/3 e. 10/3
Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175
1.
The mean height of 15-year-old boys (in em) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are nomally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys would be higher than the mean height of the sample of girls 18: O 0 9878 O 0.0062 O 0.9938 0 9972 Let E[X(Y-1)] 10, E[X(Y#1)] 20, V(X) Then E(Y) 8. V(Y) 12 and V(X+Y) 30. O 14/5 12/5 2
1. Six batteries taken at random from a large lot were subjected to life tests with the following results: 19, 22, 18, 16, 25, and 20 hours. Find the probability that the sample mean of x= 20 hours, as observed here, or one less than 20 hours could arise if the true mean of the lot of batteries is 21.5 hours, assuming a known variance of o = 10 hours, for the individual batteries in the lot. %3D
Suppose that we have disjoint normal populations A and B with equal but unknown population variances. Suppose we plan a sample of size 12 from from population A and a sample of size 6 from population B which we will pool to form the pooled variance. If the sample variance for the sample from population A is 25 and the sample variance for the sample from population B is 36, then what is the pooled sample variance?

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