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- 10#1. X is a continuous random variable distributed Beta with a =2 and B-1. a. For a random sample of size n=3 from this distribution find the pdf of the median. b. What is the E[median]? c. For a random sample of size n=3 from this distribution find the joint pdf of Yı and Y3, where Yı is the first order statistic and Y3 is the last order statistic. d. Find the pdf of R= Y3 - Y1. (R is called the range) e. Find the mean and variance of R.#7. Suppose that X has a gamma distribution with mean 12 and variance 36. (a)Give the pdf of X. (b)Find P(X > 15) using the relevant summation.
- 12) A metal bar is heated, and then allowed to cool. Its temperature T (in °C) is found to be The time is in minutes. T=15+75e-0.25 t Find the time rate of change of temperature after 5.0 minutes. 13) The standard normal curve (sometimes called the bell curve) in statistics looks like: 1 -x² y = e 2 √2π Show that there are two inflection points at x = +11. Let x = 1.442 and y = 1.450. Compute the relative error in x E y = fl(fl(x) – fl(y)) using rounding and two decimal digits.Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit 1 upper limit 2 margin of error 3 (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal σ is known the distribution of weights is uniform σ is unknown (c) Interpret your results in the context of this problem. 1% of the intervals created using…
- (a) Let X be a normal r.v. with mean u =12 and standard deviation o = 1.5. Find P( X 13 ) = (c) Let X be a normal r.v. with mean u =7 and standard deviation o = 1.5. Find P( 514. Show that for the Gamma distribution e dp = dx, 0c) Consider the following table: i 1 2 3 4 5 6 7 8 9 10 R₁ 0.7329 0.9755 0.6761 0.0917 0.1584 0.2858 0.8564 0.3628 0.4337 0.5822 Assuming an M/M/1 setup, a service rate of 18 customers every 5 minutes, and a traffic intensity of 0.95 for a pdf characterized by the exponential distribution, compute the correpsonding variates.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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