Suppose that the random variable X has mean u and variance o >0. What are the values of a and b>0 such that the random variable Y=a+bX has mean 0 and variance 1.
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- Suppose that X is a random variable with mean 30 and standard deviation 4. Y is a random variable with mean 50 and standard deviation 8. Assume the correlation between X and Y is 0. Find the varience and standard deviation of random variable Z for each of the following cases. 1) Z= 35-10X 2) Z= X+Y 3) Z= -2X - 2YSuppose 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 OTHERSSuppose that X1, X2, X3 and X4 are all independent random variables, each with a normal distribution with mean 9 and variance 25. Define X-bar = (X1 + X2 + X3 + X4) / 4. Find Prob(X-bar > 10).
- There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable Z is the sum of X and Y. That is, Z = X + Y. Calculate the mean of Z.A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance o of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of o = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 15.4 months %3D (squared). Using a 0.05 level of significance, test the claim that o? = 23 against the claim that oʻ is different from 23. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?Previous Probletn Let X and Y be independent random variables. Suppose X has variance 2 and let Y have variance 5. Find Var(3X-2Y + 3). Please answer to 2 decimal places.
- A correlation of +.20 means that [blank] of the variance in the outcome variable is accounted for by the predictor variable.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?
- Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker's times have a variance of 12.2. The second worker's times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level.What is the F statistic? (Round your answer to two decimal places.)suppose that we have disjoint normal populations A and B and we want to find the standard error estimate for estimating the difference in their means. We have an IRS from A of size 8 with variance 25 and an IRS from B of size 9 with variance 16. What is the resulting standard error estimate if we assume both populations have the same population variance?A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance o of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of o2 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 15.4 months (squared). Using a 0.05 level of significance, test the claim that o? = 23 against the claim that o is different from 23. (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit (g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.) lower limit months upper limit…