Can you please help to advise this response is correct? 8:031 of 1Example #4MSEA component has the following linear hazard rate, where t is inyearsA(t) = 0.4t,t20Extra Credit10 pts on a Testa) Find R(t) and determine the probability of a componentfalling within the first month of its operationb) What is the design life if a reliability of .95 is desired?Ginen hazard Rateat) = 0.4talt') = So.ut dtS%t dt- /5 Stde%3Da) RG) =e0.000039০.११११ 6|b) RC& =?) = 0.95 -1-.0.45-1 = JA - .- 0.250.45 -1 =Jo.25- o. OSXS - -t?t= 0.S yrs =6 montlsA ecs-us.foundations.blackboard.com C

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Answered: Example #4 MSE A component has the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let y1,y2,...,y10 be a random sample from an exponential pdf with unknown parameter λ. Find the form of the Generalized Likelihood Ratio Test for H0: λ = λ0 versus H1: λ doesn't equal λ0. What integral would have to be evaluated to determine the critical value if α were equal to 0.05?
dW is normally distributed, dW has mean zero, dW has variance equal to dt. Parameter other than dw is assumed as constant. We have a representation of the geometric Brownian motion as dS/ S = µ dt + σ dW, prove µ dt + σ dW is normally distributed and find its mean and variance.
In recent years, several companies have been formed to compete with AT&T in long-distance calls. All advertisethat their rates are lower than AT&T's. AT&T has responded by arguing that there will be no dierence in billingfor the average consumer.Suppose that the average bill for current AT&T customers is $21. A statistician takes a random sample of 100customers and recalculates their last month's AT&T bill using the rates quoted by a competitor. Let X be therandom variable for the amount of a recalculated bill, and µ be the unknown population mean of X. The samplemean and standard deviation for X are $20 and $6. The statistician wants to test if µ is signicantly dierent from$21, which is the average bill for current AT&T customers (d) Using 5% signicance level, calculate the critical values of the test. Is the null hypothesis rejected?(e) The competitor would react by using dierent set of hypotheses. For example, consider H0 : µ = 19 andH1 : µ 6= 19. What…
In recent years, several companies have been formed to compete with AT&T in long-distance calls. All advertisethat their rates are lower than AT&T's. AT&T has responded by arguing that there will be no dierence in billingfor the average consumer.Suppose that the average bill for current AT&T customers is $21. A statistician takes a random sample of 100customers and recalculates their last month's AT&T bill using the rates quoted by a competitor. Let X be therandom variable for the amount of a recalculated bill, and µ be the unknown population mean of X. The samplemean and standard deviation for X are $20 and $6. The statistician wants to test if µ is signicantly dierent from$21, which is the average bill for current AT&T customers.(a) The statistician wants to formulate hypotheses in favor of AT&T. State the hypotheses.(b) Calculate the t-statistic. Under what signicance level, among 1%, 5% and 10%, is the null hypothesis rejected?(c) Calculate the…
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
Suppose X and Y are independent, exponentially distributed random variables with rate parameter λ, λ > 0. Find the joint PDF of U and V , where U = X + Y, V = X/Y.
An industrial product is packaged in batches of units each. The number ofdefective units within each batch is unknown. Since checking whether aunit is defective or not is expensive, the quality control consists in selectingunits of the batch and obtaining an estimation of the number of defectiveunits within the batch. The batch is rejected if the estimated number ofdefective units exceeds . a. Find the moment estimator of the number of defective units within aparcel.b. If N=20, n=5, and among these units 2 of them are defective, is thebatch rejected?
Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size nfrom a distribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere. Show that thekth order statistic Yk has a beta pdf with parameters α = k and β = n − k + 1.
A projectile is launched at an angle theta with respect to the surface with velocity v0 (deterministic). If the angle of inclination is a uniform random variable in [0, pi/2 ], calculate the distribution function of the variable R defined as the point of impact of the projectile on the ground, measured from the origin. Also calculate your expected value
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