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- The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 7. (a) Compute the probability that more than 12 customers will arrive in a 2-hour period. (b) What is the mean number of arrivals during a 2-hour period.Explain the steps if you canLet X be b(2, p) (binomial distribution). Assume P(X > 1) = (a) Find p. (b) Compute P[X = 2]. %3D
- Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15A random variable X is distributed as Poisson distribution with λ = 3.5. Usethis Poisson distribution (Table A.3) to determine the following probabilities: (a)P(X < 5), (b) P(2 ≤ X ≤ 6), (c) P(X > 7), (d) P(X ≥ 5).23. Find the cumulant generating function of gamma distribution and obtain various cumulants.5. Assume that X is a discrete random variable with cumulative distribution function (cdf) F(x) given below. F(X) 0-8 0.b t0.2 -2 2 3 ->The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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