Let X and Y be independent random variables representing the lifetime (in one billion years) of Type A and Type B stars, respectively. Both variables have exponential distributions, and the mean of X is 3 and the mean of Y is 11. What is the variance of the total lifetime of three times a Type A star and a Type B star?

What is the Discrete Variable Variance for the following numbers:x = 0 and P(X = x) = 0.19x = 1 and P(X = x) = 0.27x = 2 and P(X = x) = 0.21x = 3 and P(X = x) = 0.33

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?

You run a house flipping business where you buy thousands of houses across the country, hire contractors to fix them up, and try to sell them. For any given house, you figure there is a 50%/50% chance of gaining 60% or losing 40%. This means your expected return per house is 0.5x0.60+0.5x(-0.40) = 0.10 = 10%. The variance per house is 0.5x(0.60-0.10)2 + 0.5x(-0.40-0.10)2 = 0.25. If the covariance between houses is 0.10, what is the variance of your portfolio of thousands of houses

In a human population, the proportion of individuals with a certain disease is 0.10. if we select a sample of size 1000 from this population, determine the value of the variance of the sample proportion.

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.

4. Review the variance function for specific distributions. For Bernoulli, Poisson, Gamma, and Inverse Gaussian, what does the variance function say about our ability to predict the range of possible values? (This may be a little bit challenging; give it your best guess.)

Experiment 3: Fifteen female CSCC students and 10 male CSCC students are randomly selected to determine if the mean time studying for females is significantly more than the mean study time for males. It can be assumed that all study times are normally distributed.  Are these samples independent or dependent? Find the null and alternative hypothesis.    H0:    Ha:

SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: G = 35 months,SG2 = 900Metropolis: XM = 50 months, SM2 = 1050 Referring to Scenario 10-3, suppose a = 0.01. Which of the following represents the result of the relevant hypothesis test? A) Insufficient information exists on which to make a decision. B The null hypothesis is rejected. The alternative hypothesis is rejected. D) The null hypothesis is not rejected.

Question # 20. Two college instructors are interested in whether or not there is any variation in the way they grade math exams. They each grade the same set of 30 exams. The first instructor’s grades have a variance of 52.3. The second instructor’s grades have a variance of 89.9. Test the claim that the first instructor’s variance is smaller. (In most colleges, it is desirable for the variances of exam grades to be nearly the same among instructors.) The level of significance is 10%.