1.The article "Reliability of Domestic-Waste Biofilm Reactors" (J. of Envir. Engr.,1995: 785–790) suggests that substrate concentration of influent to a reactor isnormally distributed with u = 0.3 and o =0.06.What is the probability that the concentrationa. exceeds .25?b. is at most .10?c. lies between 0.15 and 0.35?

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Answered: 1.The article "Reliability of…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A large population (consisting of measurements of diameters of ball bearings) has mean u and standard deviation o, neither of which is perfectly known. A random sample of size n = 25 observations will be taken, namely the diameters U1, U2, ·.., U25 will be observed. In other words, U1, U2, · .., U25 are independent and identically distributed random variables with u = E(U1) and Var(U1) = o². No further knowledge about the shape of the distribution is known. Define, 25 1 X 25 Ui 25 i=D1 (i) If someone says E(X 25) = 13, what information does he give you about u, if any? (ii) If someone says o = 5, what is Var(X25)? • (iii) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than the population mean u? In other words, find an approximation of P(X 25 < u). [Hint: see if the value of o is relevant or not to answer the question.] (iv) In part (iii) while approximating what theorem did you use, if any? • (v) What is the chance, approximately, that…
c) Answer both of the following: i) Consider a random variable X which is normally distributed with mean zero and unit variance. Using the proper statistical table, find the number z such that P(z < X < 2.64) = 0.4760. Give your answer rounded to 2 decimal places. follows at distribution with (2n + 1) degrees of freedom, i.e. Y ~ t2n+1- ii) A random variable Make use of the appropriate statistical table to get the value of n knowing that P(Y 2 3.1824) = 0.025.
7. Conduct a complete hypothesis test: Researchers have often noted increases in nonviolent crime during the warm weather months. Over the past 30 years, a particular precinct has noted an average of u = 14 nonviolent crimes during the summer months. Assume the distribution is nearly normal with o = 3. For a sample of n = 4 weeks in which the daily temperature was extremely hot, the weekly average of non-violent crimes was M = %3D 17.25. g. Is there a significant difference in the number of non-violent crimes during hot weather days compared to typical days? Test at the alpha = .05 level. j. What is the probability that we made a Type I error? What would this probability be in terms of the independent and dependent variables? k. Is there a risk of a Type Il error? Explain.
(8)(1)
answer With details pls. can you explain the difference between the E(Yn) E(Yi) and E(Y(n)) .
Please show step-by-step explanations. Thank you
7.4.1
1. (See Handout 1, Example 1). The life expectancy of a particular brand of lightbulb is normally distributed with a mean of 1500 hours and a standard deviation of 75 hours. We want to calculate the probability that a lightbulb will last more than 1440 hours. a) Calculate the critical z-score. b) Label the axis and shade the area under the curve that we are interested in. Hours z-score c) What is the probability that a lightbulb will last more than 1440 hours? d) What is the probability that a lightbulb will last less than 1440 hours?
3. Let X1,X2, ..,X, be a random sample form a normal distribution with E(X;) = µ;and Var(X;) = o². Assume s? = E(X;_ X)²/n and s3 = (n/(n – 1))s?. Questions: a. Compare between the estimators si and s?. b. Which one you preferred? What is (are) your reason(s). 4. Let X1,X2, . X, be a random sample form a uniform distribution, f(X)e = 0*(1– e)!-*; 0 < x < 1. Assume T1 = X1 and T, = (-)Ex;. %3D a. Check the unbiasedness property for T1 and T,. b. Find the MSE of T, and T,. Can you preferer one of them? Discuss your reasons. с. 5. Suppose that X, X2,. , X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+ X8); -1< X <1. Show that 3x is a consistent estimator of e.
4.3 Assume that x is normally distributed. At a fixed operating setting, the pressure in a line downstream of a reciprocating compressor is known to maintain a mean value of 12.0 bar with a standard deviation of 1.0 bar based on its history. What is the probability that the line pressure will exceed 13.0 bar during any measurement? 4.4 Consider the toss of 4.
Let X,, X,, and x, represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values 4,, Hz, and uz and variances o,2, 0,2, and o,2, respectively. (Round your answers to four decimal places.) A USE SALT 2 (a) If H1 = H2 = H3 = 60 and o,? = 0,2 . = 18, calculate P(T, s 204) and P(144 s T, s 204). P(T, s 204) = 0.9995 P(144 s T,s 204) = (b) Using the us and os given in part (a), calculate both P(54 s X) and P(58 s Xs 62). P(54 s X) P(58 s Xs 62) = 0.568 0.568 %3D (c) Using the u's and o's given in part (a), calculate P(-12 s X, - 0.5X2 - 0.5X3 s 6). P(-12 s X, - 0.5X, - 0.5x, s 6) = 0.8665
How many even four-digit numbers can be formed from the digits 0, 1, 2, 5, 6, and 9 if each digit can be used only once?

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