Let N be a Poisson random variable with mean A. Determine the Chernoff bound for N. Compare the Chernoff bound for A 10 to the actual value of P{N> 20}, which you can numerically evaluate using Matlab. =
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- Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?Let A be a random variable corresponding to the sum of the outcomes of two independent rolls of a fair 6-sided die (numbered from 1 to 6). Determine the variance of A.Let X be a random variable corresponding to the number of shoppers that enter a mall at a given time of the day. It X is known to be a Poisson variable with an average of 10 shoppers per minute, determine the probability that there are 12 shoppers who will enter the mall in the next 90 seconds. Select the correct response: 0.1024 0.0829 0.0956 0.1298
- Suppose that the test score of a student taking the final of a probability course is a random variable with mean 67.9. (a) Give an upper bound for the probability (in three decimal places) that the student's test score will exceed 95. Answer:Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…Suppose X is a binomial random variable characterized by the parameters n = 9 and p = 0.77. Find P( X = 6 ). Round your answer to three (3) decimal places. Your Answer:
- Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.f. Why are the estimated waits in this system so long? Are the assumptions behindthem reasonable? Why or why not?Let x be a binomial random variable with n = 14 and p four decimal places. 0.3. Find the following. Round each answers to P(X = 8) Р(X 10) = P(4 < X < 9) =
