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For a Gaussian random variable, derive expressions for the coefficient of skewness and the coefficient of kurtosis in terms of the mean and variance µ and σ2.
Explain the double-negative logic of hypothesis testing (eg: a scientist fails to reject the null hypothesis). What is the five-step process for hypothesis testing? Is the order important? Why or why not?
The scores of the GRE exam are transformed so they have a mean of 500 and standard deviation of 100. The scores are known to be normally distributed. What is the percentage of students that score below 750?
Examine the plot of the regression residuals against t. Is there a tendency for the residuals to have long positive and negative runs? To what do you attribute this phenomenon?
Evaluate 2-month moving average and Exponential smoothing by MAD.
Construct a graph of the probability distribution of X. What is the probability that a child receives exactly three diagnostic services during and office visit to a pediatric specialist?
Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?
Identify the sampling techniques used, and discuss potential sources of bias(if any). Explain.Using random digit dialing, researchers call 1400 people and ask what obstacles keep them from voting.
Following Example 4.21, let X and Y denote the arrival times of the first two calls at a telephone switch. The joint PDF of X and Y is
What is the 95% confidence interval for the mean number of weekly hours that United States adult use computers at home? Show work.
What is the probability that none of them has lost electricity in his/her household? Assume that their locations are spread out so that loss of electricity is independent among their households.
q1.a multiple-choice test consists of 12 questions with 4 possible answers to each question. in how many ways can the
Assume that the population is normally distributed. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from months?
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