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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.
If there is relationship between parental income and SAT score, why can't we bring to a close that differences in score are caused by differences in parental income.
Suppose a sample of 35 surveys shows a sample mean of 17 minutes. Use = 4 minutes. Is the premium rate justified? Formulate the null and alternative hypotheses for this application.
A survey of 500 non-fatal accidents showed that 226 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.
Research at the University of Toledo indicates that 50 percent of the students change their major area of study after their first year in a program.
A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.
Is there a significant difference between the scores between the Republicans and the Democrats?
Experience has shown a company that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment but guarantees to refund the charge if delivery is not made within 24 hours.
A sample of 25 their average life from the time they are fully charges to the time they are fully discharged is 170 minutes the sample standard deviation is 30 minutes. Test the claim that battery will last for three hours.
If the organization's claim is correct, what is the probability of having a sample mean of or less for a random sample of this size?
You are asked to match three songs with the performers who made those songs famous. if you guess, the probability distribution for the number of correct matches is:
Choose one of these tests and describe in your own words, the purpose of the test, any particular assumptions or limitations pertaining to the test, and provide an example where you could employ the test.
What is the probability that two of absent students were girls.What is the probability that two of absent students were boys.
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