The moment generating function of the negative binomial distribution is given by pe' m, ()=1-ge 1- qe' Derive the mean of the distribution using the mgf.
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- The local news reported that 6% of U.S. drivers text on their cell phones while driving. If 300 drivers are selected at random, find the probability that exactly 25 say they text while driving. Be sure and use the continuity correction for the normal approximation to the binomial distribution.Show that if ν > 2, the chi-square distribution has arelative maximum at x = ν − 2. What happens whenν = 2 or 0 <ν< 2?The number of babies in a litter of rabbits is approximately Poisson distribution with mean 6. Litters can occur once per month for a 9 month period (3 months infertile). What is the standard deviation of the number of babies in one litter? What is the probability of a litter with exactly one rabbit? What is the approximate probability that over a 9 month period, a rabbit will have more than 65 babies (use the Central Limit Theorem, continuity correction is optional)? Incidentally, the plot at right shows the exact Poissondistribution you’ll be using, and you’ll note it looks quite a bit like some other distribution . .
- Find kurtosis by using ungroup data given in the picture using quartile deviation, make sure to arrange data before solving question.Obtain the moment generating function of exponential distribution. Hence find mean and standard deviation.In a café, the manager wishes to estimate p, the proportion of customers who will order sandwich for their lunch. Suppose 30 out of 300 customers will order sandwich for their lunch. Find the probability that more than 40 customers will order sandwich for their lunch by using a suitable approximation
- The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute Within what limits does Tchebysheff's Theorem suggest you would expect the number of visits to this website to lie at least 75% of the time?In kurtosis, the bell shaped distribution called mesokurtic if the frequency looks more peaked than normal. True or false?A researcher believes that about 74% of the seeds planted with the aid of a new chemical fertilizer, will germinate. He chooses a random sample of 90 seeds and plants them with the aid of the fertilizer. Assuming his belief to be true, approximate the probability that Atmos 66 of the 90 seeds will germinate. I use the normal approximation to the binomial with a correction for continuity.
- Among people who subscribe to the Sacramento Bee Newspaper, 40% have a college degree. If a simple random sample of 100 people is drawn from the Sacramento Bee's subscribers, what is the probability that more than 45 have a college degree? (Use a normal approximation with a continuity correctionand show your work!)The number of birth defects in a region is commonly modeled as having a binomial distribution, with a rate of four birth defects per 100 births considered a typical rate in the United States. What is the probability that a county that had 200 births during the year would have between 4 and 12 birth defects. Use both the binomial distribution and the Normal approximation with the appropriate continuity correction from the table below. Is the normal approximation reasonable?The number of eggs that a female fly lays in her lifetime is normally distributed with a mean of 800 eggs and a standard deviation of 100 eggs. If a random sample of 15 flies is chosen, find the mean and standard eror of the mean using the Central Limit Theorem.