Let Y be a random variable having characteristic function Find () EX] (1) E[X²] (m) Var[X] 0.8 1-0.2
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Let Y be a random variable having characteristic function
Find
(1) E[X]
(1) E[X²]
(m) Var[X]
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- Consider that a pdf of a random variable X is 1 -25x53 fx (x) ={K otherwise and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and ( d) EΧΥ.Let X1,..., Xn be a random sample from a uniform distribution on the interval [20, 0], where 0 0. Let X(1) < X(2) <...< X(n) be the order statistics of X1, ..., Xn.Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1
- f(X)= 3/8( 4x - 2x2 ) 0<* x <* 2 (* less or equal to) a. Find the variance of X.(b) Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by f(x)=K(6-x), 0Suppose 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 ≤ TDerive the following:(c) variance(d) moment generating functionQ1 Let X1, .. X, f(r;0) = (;)*"(1 – 0)-,1 = 0, 1,2. %3D (i) Find the score and information functions of 0. (i) Show that X is an efficient estimator 0. إضافة ملفThe continuous random variable X on [-1,1] has pdf given by fx(x) = k(3x + 5) for x = [1,1] where k is a constant that you are going to determine. fx(x) = 0 outside the interval [-1,1] Hint: consider Calculate the following: i. k ii. E(X) iii. Var(X)Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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