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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.Show that there are no values of c such that f(x) = cx can serve as the values of the probability distributionof a random variable with the countably infinite rangex = 1, 2, 3, ...24. Let X1, X2, ., X 100 be a random sample of size 100 from a distribution with density .... f(x) = {0 for æ = 0, 1, 2, .,00 otherwise. What is the probability that X greater than or equal to 1?
- 2.) For a continuous random variable X,where c is any one isolated number what is: P(X = c) Hint: For continuous random variables we always calculate things like: P(aLet X, and X2 be independent exponential distributions with the same parameter 2. What is the joint distribution of Y, = X, + X2 and Y, X1 -? What are the distributions of Y, and X1+X2 Y2?5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX210. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf f₂ (ylx) of Y.. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours. d) Given that a Type B bulb fails at 300 hours, find the probability that a Type A bulb lasts longer than 300 hours. e) What is the expected total lifetime of two Type A bulbs and one Type B bulb?2.5.5.) The cumulative distribution function F(x) of a random variable X is given by 0, -8Show that, if the random variable X has an F-distribution with ν1 and ν2 degrees of freedom, then Y =1Xhas an F-distribution with ν2 and ν1 degrees of freedom.Suppose X is random variable whose p.d.f. is f2)=(2x-x²), 0, OSxs2 Suppose X is random variable whose p.d.f. is f(x)={4 elsewhere Find the mode , if it exists.For what values of k canf(x) = (1 − k)kx serve as the values of the probability distribution of arandom variable with the countably infinite range x =0, 1, 2, ...?4. Assume that X is an exponential random variable. Suppose further that Var(X) = 5. E(X). (a) Find the parameter 0> 0. (b) Compute Var(X + 4). (c) Compute P(X > 15[X > 11).SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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