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Using the fact that 1+x = 4+(x-3), find the Taylor series about 3 for g. Give explicitly the numbers of terms. When g(x)=square root of 1+x
Check the first four terms in the Taylor series above and use these to find cubic Taylor polynomials about 3 for g.
Use multiplication of Taylor series to find the quartic Taylor polynomial about 0 for the function h(x)=(cosx)ln(1+x) evaluating the cefficients
A fellow researcher fits a simple linear regression model Yi = α + βXi + ui by least squares, but has doubts that the first least squares assumption E(ui |Xi) = 0 is correct for her data set.
The Problem Solving Inventory (PSI) has a normal distribution with mean = 90 and standard deviation = 15. A researcher suspects that the mean for female students is higher than 90.
Compute the sample variance and sample standard deviation as a measure of volatility of monthly total return for Chevron (to 2 decimals): Sample variance and Sample standard deviation.
The mean time for the completion of a shopping center is estimated to be 14 months with standard deviation = 4 months. What is the probability that the renters will not be able to move in 19 months?
Dertermine the probability that a male is a Major or a Colonel?
Which approach is most preferred and why? Optimistic, conservative, or minimax regret. Also, is establishing the most appropriate approach before analysising the problem important for the decision maker?
Salary data for a sample of 50 universities were obtained. We are curious about the relationship between mean salaries for assistant professors.
What are the null and alternate hypotheses? How many treatments are there? What is the critical value of F at the 5% level of significance? Indicate in words when you would reject the null hypothesis.
The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes.
Each vehicle had the gallon of gas added to the empty tank and then driven until empty. Number of miles travelled for all twelve readings are below. Use data to compute the mean and median mileages.
Suppose that 30% of the population has black hair. In a randomly-selected group of six people, how probable is it that
Suppose you want to test the claim that population mean miu=3.5. Given a sample size of n=34 and a level of significance of alpha=0.01, when should you reject Ho?
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