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1. Prove that a and b are coprime if and only if no prime numbers divides both a and b
2. Show that [a,m] = m if and only if a divides m
Statistics and Probability, Statistics
1. A stock market analyst is able to identify mis-priced stocks by comparing the average price for the last 10 days to the average price for the last 60 days. If this is true, what do you know about the market's efficien ...
New York graduates tend to leave the state after graduating. A study asked the students of NYU "Are you planning to stay in NY after graduation?" In the sample, only 37% answered yes. The study explained that with a 95% ...
A carnival game involves a spinner that is designed so that in 20 percent of spins the player will win a prize. A random sample of 100 spins will be observed and the random variable X = number of times in the sample that ...
Let X be a random variable with range RX = {-1, 0, 1} and let P(X = 1) = P(X = -1) = p/2 for some p ∈ [0, 1]. a) Compute P(X = 0). b) Compute the expectation E[X] and variance Var(X) of X as a function of p, and determin ...
With whom should you consult about design strategies to improve products/services and why would you consult with these individuals or groups?
1) It appears that new car purchases have peaked in 2018 vs. used car purchases. The following probability distribution table shows the random variable x, where x is the number of new cars purchased by household during t ...
Suppose a machine has two components that prevent injury; component A and component B. If either of the components fail, an employee will be injured. It is important to note that both A and B cannot fail at the same tim ...
Research Scenario: A community psychologist is interested in whether people's self-reported degree of religious belief predicts their self-reported feelings of well-being. She administers two questionnaires to 17 individ ...
There are 20 total socks, 10 white and 10 black. This makes 10 total matching pairs of 5 pair of white and 5 pair of black. If each time you pick a sock from the drawer a sock just like it magically replaces it, what is ...
Fifty-seven percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random va ...
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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