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a. Give at least two important uses of the moment generating function (mgf) of an rv.
b. Could M(t) = 1/2 e^(-2t) + 2/5 e^(-t) - 2/5 be the mgf of a discrete rv X? Explain
c. If the discrete rv X has mgf M(t) = (1 - 2t)^(-2/3), find E(X) and Var(X).
What is the value of the population mean? What is the best estimate of this value?
Popcorn kernels take between 100 and 200 seconds to pop. What sample size (number of kernels) would be needed to estimate the true mean seconds to pop with and error of 5 seconds and 95% confidence level?
Using a 1% level of significance, can the hypothesis that the distributions for the student's scores are identical be accepted?
Find the critical value and test statistic value follows normal distribution.
Check that the formula (1) holds when X Unif(0, b). Formula (1) also works for b = 1. Check this when X is an Exponential RV with PDF f(x) = e-x for x 0.
Correlation between the two variables - Evaluate the value of the correlation coefficient.
About 95% are between 500 +- 200; i.e. between 300 and 700 Where is the data located? Where is the "middle" of the data? How variable are the data? How spread out about the "middle" are the data?
why the harvard nurses health study is an observational study. discuss whether it would be probable to gather similar
In addition, the gender of the respondent is noted. After analyzing the results the following table of joint probabilities was produced: Find the probability that a customer who rates Windsor as excellent is a man. 0.45
What can we conclude from this summary, Which of the following statements is correct and In which of the following situations would permutation tests be suitable
Determine the critical z values. Suppose that normal distribution applies. Right-tailed test; standard deviation = 0.04.
How much better are the workers at one plant compared to another? How much "better" is line 1 of variety A compared to line 2 of variety C?
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