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The continuous random variable X has probability density function (pdf) given by
Show that, subject to t < 1, the Moment Generator Function, MGF, of X is:
Use the series expansion method of the MGF to find E(X), E(X2) and E(X3), the first three moments of X about the origin. Use your results to show that the mean and variance of X are both equal to 2. The standardised third moment, b3 = E{ (X - m)3 ÷ s3 }, provides a measure of skewness in the distribution of X. Determine the value of b3 for this distribution. Using a suitable distributional approximation, find the probability that the mean of a random sample of n = 25 observations will exceed 2.5.
You have been asked to develop a study of the effects of watching Sesame Street on childrens' gender role orientations, intelligence, or sociability.
Construct a 90 percent confidence interval for the true mean weight. Describe factors which might cause variation in the weight of Tootsie Rolls during manufacture.
When 319 college students are arbitarily selected and surveyed, it is observed that 120 own a car. Determine a 99% confidence interval for true proportion of all college students who own a car.
At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population was greater than 0.10? Discuss the underlying assumptions of the test used in (a)
At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol.
A study of 35 professors showed that the average time they spent creating test questions was 13.5 minutes per question. The standard deviation of the population is 3.8. Which of the following is the 99% confidence interval for the average number o..
Conduct a two-tailed hypothesis test given the information below. Assuming that the population variances are equal for male and female Grade Point Averages (GPAs), use the following sample data to test.
A cut-off time is set at the slowest 10% of the learning distribution. Anyone slower than this cut-off time is definitely not hired. What proportion of the candidates will be hired automatically?
A chi-square test for goodness of fit is used to test whether or not there are any preferences among 3 brands of cola.
A pair of dice is tossed once. Let X denote the sum of the face values, and let Y denote the absolute value of the difference between the face values.
The following frequency distribution was obtained. The data values are in hours. Construct a histogram for the data .
Calculate the mean absolute deviation based on the 2-day moving average. You can have a forecast and an actual temperature.
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