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Q1. Consider the sets X = {4m + 1|m ∈ Z} and Y = {2n - 1|n ∈ Z}.
(a) Prove that X ⊆ Y.
(b) Is Y ⊆ X? If yes, prove it. If not, find an element of Y that's not an element of X.
Q2. Let X be a set, and P(X) its powerset. Define a function f : P(X) → P(X) by f(A) = X\A.
(a) Consider the case X = {1, 2, 3}. Evaluate f(A) for every A ∈ P(X).
(b) For X any set, prove that f is a bijection.
Check in each case whether the values of n and θ satisfy the rule of thumb for a good approximation, an excellent approximation, or neither when we want to use the Poisson distribution to approximate binomial probabilities.
A survey of top executives revealed that 35 percent of them regularly read Time magazine, 20 percent read Newsweek, and 40 percent read U.S. News and World Report.
given a normally distributed population with u 80 and 05. what is the probability of randomly drawing a score that
Constructing the ANOVA table. Seven explanatory variables are used to predict a response variable using a multiple regression. There are 140 observations. Write the statistical model that is the foundation for this analysis. Also include a descri..
During 2008, college work-study students earned a mean of $1478. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $1503 during that year
L.J. Raney & Associates is a financial planning group in Kansas City, Missouri. The company specializes in financial planning for schoolteachers in the Kansas.
What is the probability that the average of the scores of the two students from university A will be greater than average of the scores of the three students from University B?
Binomial setting? A binomial distribution will be approximately correct as a model for one of these two settings and not for the other.
assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 15.find
What is the role of interest rates when firms make investment and consumption decisions? Please explain
The capacity of the fuel tank of the 2007 Volvo S40 is designed to be 12.625 gallons. The actual capacity of tanks produced is controlled using a control chart.
If the liquidity premium theory of the term structure of risk-free rates holds, what is the liquidity premium for year 2, L2?
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