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Let X and Y be jointly Gaussian random variables.
Show that is also a Gaussian random variable.
Hence, any linear transformation of two Gaussian random variables produces a Gaussian random variable.
Statistics and Probability, Statistics
If an Urn1 contains 6purle balls and 4red balls. And Urn2 contains 4purple balls and 6 red balls. Urn3 contains 4purple balls and 5red balls. If one of the urns is selected at random and a ball is drawn, what is the prob ...
A random sample of 34 taxpayers claimed an average of ?$9,623 in medical expenses for the year. Assume the population standard deviation for these deductions was ?$2,441. Construct confidence intervals to estimate the av ...
Acme Airlines flies airplanes that seat 20 passengers. From experience, they have learned that, on average, 85% of the passengers holding reservations for a particular flight actually show up for the flight. If they book ...
Buses run every 15 minutes along a certain route during rush hour. The time that a person would have to wait at a bus stop is uniformly distributed between 0 and 18 minutes. a. What is the probability that this person ha ...
A researcher wants to determine if there is an association between religious affiliation (e.g., Christian, Muslim, Jewish. Buddhist, Unaffiliated, etc.) and ethnicity (African American, Asian, American Indian, Whte, Othe ...
Micron Technology Inc. invested into 7 new projects (all of equal size). For each of these project, there is a 75% probability that the project will have a 12% return and a 25% that it will have a -9% return. Each of the ...
If you flip five coins what is the probability that you will get at least three heads?
A logging truck sales representative will phone either one or two potential buyers per day with probabilities of 0.25 and 0.75, respectively. Each contact will result in either no sale or a $75,000 sale with probabilitie ...
Suppose you just purchased a digital music player and have put 9 tracks on it. After listening to them you decide that you like of the songs. With the random feature on your? player, each of the 9 songs is played once in ...
In a certain city, a school administrator hypothesized that students enroll in school within 5 km from their homes. To check this claim you asked 30 student from the said city and you found that the mean distance between ...
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Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate
Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p
Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As
Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int
Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As