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1. Show that if Z1 and Z2 are independent standard normal random variables, then for all ρ (correlation), Z1 and ρZ1+sqrt(1-ρ2)*Z2 are standard normal with correlation ρ.
2. Show that for all ρ and v, T1 = (Z1)/sqrt(X/v)and T2 = (Z2)/sqrt(X/v) have correlation ρ, where Z1and Z2 are standard normal with correlation ρ, and X is independent of both Z1 and Z2 and has a Chi-Squared distribution. (for simplification use the fact that T1 and T2 both have the t distribution with v degrees of freedom and conditional expectations.)
(v=degrees of freedom)
a bank has the following data on the gender and marital status of 200 customers: single 20 male 30 female, married male 100 female 50,
The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures.
Assume X is an exponential random variable with parameter lambda. Find the method of moments estimator for lambda.
If the sample standard deviation is s = 10, are the data sufficient to conclude that the treatment has significant effect using a two-tailed test with α = .05?
Suppose that the probability is 1 in 3,900,000 that a single auto trip in the U.S. would result in the death of the driver. Over a lifetime, an average U.S. driver takes 50,000 trips.
Researchers at Pharm-X, a pharmaceutical company, are testing and comparing the effects of Drug A and Drug B on participants' allergies. The researchers are using a double-blind procedure to conduct their test.
The personnel manager at a company wants to investigate job satisfaction among the female employees. One evening after a meeting, she talks to all 30 female employees who attended the meeting.
At one excavation site 8641 pot shards have been found that not yet been cleaned and identified. What is the probability that:
The Weschsler IQ test has a μ =100 and a σ = 15. A vitamin company said if people took vitamin X for 30 days their IQ would improve. A simple random sample of 49 people took the vitamins for 30 days. They then took the IQ test. The mean IQ of the ..
Use MegaStat's output for simple linear regression to determine the regression equation
Office Visits what is the age distribution of patients who make office visits to a doctor or nurse?
Public health statistics indicate that about 26.4% of Americans smoke. Suppose a random sample of 50 people is selected. Approximate the distribution of the same proportion with the normal model.
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