fx₁x (*19) = {20 Че-х-у іє хну что otherwise 192²} Find fycy) and fx (x) where fxiy (xiy) is joint pdf and fycy) / fx(x) are marginal distribution functions WARS
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- Let X * b(4,) find Var(3x) and distribution function.(26) Let X b (8,-) find Var-x) and distribution function.A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows: f(x) = kx^2 if 0 <= x <= 2, and 0 otherwise. (a) What is the probability that the lecture continues beyond the hour for between 30 and 90 sec? (Round your answer to four decimal places.) (b) What is the probability that the lecture continues for at least 105 sec beyond the end of the hour? (Round your answer to four decimal places.)
- The pdf is given as follows: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.Let the pdf of X be f(x)=3x^2, 0<x<1. Find the probability that X is greater than 0.3.(26) Let X b(8,- Var-x) and distribution function.
- The moment generating function of X is given as follows: M(x)(t)= e^(8t). Use the moment generating function to find the mean of X.'Time headway' in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) = {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?Let iid * Irwin- Hall distribution(n) 2n Find the pdf of S = E X;. X1,, X, (수): (4" with MGF Irwin- Hall distribution(2nk) Irwin- Hall distribution(3k) Irwin- Hall distribution(2n + k) Irwin- Hall distribution(3n) None
