Let X and Y be independent random variables representing the lifetime (in one billion years) of TypeA and Type B stars, respectively. Both variables have exponential distributions, and the mean of X is3 and the mean of Y is 11. What is the variance of the total lifetime of three times a Type A star anda Type B star?

Given data is mean of X is 3mean of Y is 11we have to find the variance of the total life time of 3…

Answered: Let X and Y be independent random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with P(A) = 0.3, P(B) = 0.3, and P(C) = 0.4. (a) Among the next 210 customers, what are the mean and variance of the number who pay with a debit card? E(X) = V(X) = Explain your reasoning. This answer has not been graded yet. (b) Answer part (a) for the number among the 210 who don't pay with cash. E(X) = V(X) =
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.)
Suppose for 40 observations the variance is 50. If all the observations are increased by 20, the variance of these increased observations will beA. 2.5B. 50C. 70D. 400
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:
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The nation of Olecarl, located in the South Pacific, has asked you to analyze international trade patterns. You first discover that each year it exports 10 units and im- ports 10 units of wonderful stuff. The price of exports is a random variable with a mean of 100 and a vari- ance of 100. The price of imports is a random variable with a mean of 90 and a variance of 400. In addition, you discover that the prices of imports and exports have a correlation of r = -0.40. The prices of both ex- ports and imports follow a normal probability density function. Define the balance of trade as the difference between the total revenue from exports and the total cost of imports. What are the mean and variance of the balance of trade? What is the probability that the balance oft trade is negative?
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.
Ensure the RaceResults worksheet is active, then use the FREQUENCY function to calculate the frequency distribution of the race results in column D. Place your results in the range G4:G9. Enter a function in cell F22 to calculate the correlation between age (Columns C) and race time (Column D). Enter a function in cell G22 to calculate the covariance between age and race time. Enter a function in cell H22 to calculate the variance of the ages in the data set. Note this is a sample of data not a population. Enter a function in cell 122 to calculate the standard deviation of the ages in the data set.
Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 15.8 pounds in the second trimester, with a standard deviation of 6.2 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p-value for the hypothesis test. The p-value should be rounded to 4 decimal places.

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