6. For a given series of paired data, the following information is availableCovariance between X and Y series = -32.6Standard deviation of X series = 8.6Standard deviation of Y series = 4.8No of pairs of observations = 15Calculate the coefficientof correlation7. The coefficient of correlation between two variables X and Yis-0.4andtheir covariance is equal to -16. If the variance of Y series is 36, find thevariance of X series.

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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 have a sample of size n for variables X and Y. The sample covariance of X and Y is Cov(X,Y) = 1,000, the sample standard deviation for X is Sx=20 and the sample standard deviation for Y is SY=75. What is the sample correlation coefficient, r?
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 - 2Y
Suppose X, Y, Z are i.i.d. from a Normal distribution with mean μ and variance 4. You have to compare between three estimators for μ, which are T1:= (2X + Y)/3 , T2:= (X + Y − Z)/2 , T3:= (Y + 2Z)/2 . (a) Which among the above are unbiased estimators for μ? (b) Which among these have the smallest variance? (c) Can you propose an estimator for μ which is better than the 3 above? You have to show that your estimator is indeed better.
A finance analyzer have come to the conclusion that he wants to purchase stocks from Company A, with an expected yield of E(X) = 4% and variance to the yield being V(X) = 0.49. Another stock from another Company B have an expected yield of E(Y) = 6% and variance V(Y) = 0.64. The correlation of the yield between the two stocks is p(X,Y) = 0.3. The finance analyzer wants to invest a portion p(0 < p < 1) into Company A stocks, and the rest (1 - p) into company B stocks. The combined investment have a yield of W = pX + ( 1 - p)Y. For p = 0.4, such that W = 0.4X + 0.6Y. What is the expected value and variance for W.
The null and alternate hypotheses are:H0: μ₁ = μ2H1: μ₁ ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 26 and a sample standard deviation of 5.0. A random sample of 8 observations from another population revealed a sample mean of 30 and a sample standard deviation of 6.0. The population standard deviations are unknown but assumed to be equal. At the 0.01 significance level, is there a difference between the population means?
Suppose we have two normal populations denoted A and B, and we want to compare their population variances by estimating the ratio: variance of population B divided by variance of population A. We have an independent random sample of size 15 from population A and an independent random sample of size 9 from population B. The sample variance for population B turns out to be 30 percent larger than that for population A. What is the 99 percent confidence interval for the ratio: population variance of population B divided by population variance of population A? Use stattrek.org for finding the needed critical values.
The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…
If X is a normal variate with mean 5 and variance 4. Find P ( -1.5 < X < 2)?
As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation (computed from the raw data) of r = 0.60 for a sample of n = 10 participants. (4 pts. total) Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05. In your response, be sure to specify the critical value for r.
One sample has a variance of s2 = 10 and the second sample has a variance of s2 = 20. If the pooled variance is computed for these two samples, then the value obtained will be.. Select one: a.exactly equal to 15 b. smaller than 10 c. larger than 20 d. somewhere between 10 and 20

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For a given series of paired data, the following information is available Covariance between X and Y series = -32.6 Standard deviation of X series = 8.6 Standard deviation of Y series = 4.8 No of pairs of observations = 15 Calculate the coefficient of correlation