11.43. The number (x) of items of a certain kind demanded by customers follows the Poisson law with parameter 9. What stock k of this item should a retailer keep in order to have a probability of 0.99 of meeting all demands made on him. Use normal approximation to Poisson Law.
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- Q1Suppose that X has a lognormal distribution with parameters 0 = 2 and w² = 9. Determine the following. %3D (a) Round the answer to 3 decimal places. P(X 1000. Round the answer to 2 decimal places.Suppose the log-ins to a company's computer network follow a Poisson process with an average of three counts per minute. What is the mean time between counts? What is the standard deviation of the time between counts? a. E(X) = 0.333, SDX) = 0.111 b. E(X) = 0.333, SD(X) = 0.333 Oc. NONE Od. E(X) = 3, SD(X) = 3
- Some previous studies have shown a relationship between emergency-room admissions per day and level of pollution on a given day. A small local hospital finds that the number of admissions to the emergency ward on a single day ordinarily (unless there is unusually high pollution) follows a Poisson distribution with mean = 2.0 admissions per day. Suppose each admitted person to the emergency ward stays there for exactly 1 day and is then discharged. The hospital is planning a new emergency-room facility. It wants enough beds in the emergency ward so that for at least 95% of normal-pollution days it will not need to turn anyone away. What is the smallest number of beds it should have to satisfy this criterion? Answer the previous question for a random day during the year.Let X~Geo(0.3). Find the following a. P(X = k). b. P(1 ≤ X 3) and describe its interpretation. d. The mean μ = E(X) and the Variance σ2 = Var (X) of the random variable X.There are 15 black balls 14 red balls and 11 white balls in a jar and you get to randomly pick one ball without looking if you draw a black ball you win $500 if you pick a red one you lose $10 if you pick a white one you lose $100 what is the expected value of picking a ball
- Help pleaseThe results of a mathematics exam at JUST university for two classes are as follows: Class 1: (n=32, mean=17, SD=8) and Class 2: (n=36, mean=7, SD=12). find the upper bound of the 95% CI for the difference in means P,- non O a. 21.7600 Ob. 5.1990 Oc14.8010 Od. 14.9110 Next pageQ3. Generate three random variates according to each of the following distributions using your own uniform random variates from U(0, 1) and list them: • Discrete Uniform: U (15, 17) • Uniform: U (0.57, 1.5). • Triangular: Triang (2, 10, 4). • Binomial: Bin (12, 0.4). • Lognormal: LN (5, 1). Beta: Beta (5, 5). • Negbin (8, 0.4) • Weibull (.5, 2.5) Geom (0.5) • PT5 (0.5, 0.5)
- Exercise 10. For an exponential random variable X (Definition 10), show that E[X] = }. More generally, for a function o : R R, E(¢(X)] = | (u) dF(u) (5.4)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.…The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. a) find the P(10<x<15) (10 and 15 are seconds) b) find the P(x>15| x>10) (10 and 15 are seconds) c) find the P(x<15) (15 is seconds)