3. Suppose W is a continuous random variable with density function if x < -1 or x > 1, fw (x) = |1- |2| if –1< ¤ < 1. Calculate øw (t) using properties of characteristic functions. (Hint: Problem 6(a) on HW8 may be useful. You shouldn't need to do much calculation.)
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- (24) Let X be a random variable with p.d.f. Ze-2 0If 2 > 0 and X is a continuous random variable with p. d.f. 22xe-dx ,x 2 0 ,otherwise f(x) = Then var(X) is:7. a) Suppose that X is a uniform continuous random variable where 07. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0der a random sample X1, X2, ..., X, having the pdf, f(r; 0) 14. Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X))> log(1/E(X)) (d) E(X³) > (E(X))³5. Let X be a positive random variable; i.e., P(X - log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³3. Let the random variable X have the moment generating function M(t) = What are the mean and the variance of X, respectively? -1 < t < 1.Show that the characteristic function of Laplace distribution ƒ(x) = 1=1/√e ²¹x²₁ е - -∞0 < x < ∞ 1 is C (0) = 1+0² Find also the mean, the variance and mean deviation about the mean. 11.Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ Tb) The probability density function of random variable X is given as: - Вх {*5 if 0 < x < 1 otherwise f(x) = If the expected value of the random variable X is 1/3. Find the values A and B.If F(x) is cumulative distrbution function of a continuous random variable X, the probability (function f(x) is the dervative of F(x (Fa)se (TrụeSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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