= 'f X is either (a) Poisson with parameter λ, or (b) (1, 2), show that the distribution of Y (X-EX)/√var X approaches the N(0, 1) distribution as → ∞. (c) Show that === (1 + ~ + 1/² - + 2! +77) → n! 1 2 as no.
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- (13) Let X b(6,-) find E(5+6x) and distribution function. 3(3) Let X = b >(8,-) find E(5+6x) and distribution function.Suppose f"(x) = N,(h) + a,h+ azh³ + azh5 + …- ... The value of N2(h) using Richardson's extrapolation is: N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order 0(h^2 ) N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^4) N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h^2) N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h^3) *
- 5. Let (*1, x2, ., Tn) be a random sample from the distribution f (x) = Ax^-1; 0 0. Find the moment estimator of A.Suppose f" (x) – N, (h) + a, h? + a,h' + azh® + … The value of N,(h) using Richardson's extrapolation is ON2 (h)=2N1 (h/2)-N1 (h) with error of order O(h^2) O N2 (n)-2N1 (h/2) NI (h) with error of order O(h) O N2 (h)-(4N1(h/2)-N1 (h))/8 with error of order O(h^2) O N2 (h)-(4N1(h/2)-N1 (1)/3 with error of order O(h^4 )Suppose f" (x) = N,(h) + a,h² + a̟h* + azh6 + •… ... The value of N2(h) using Richardson's extrapolation is: N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^2) N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^4 ) N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h) N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h^2)
- Suppose f"(x) = N¿(h) + a,h+ azh² + azh³ + •… The value of N, (h) using Richardson's extrapolation is: O N2 (h)-(4N1(h/2)-N1 (h))/3 with error of order O(h^2) O N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h^2) O N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h) N2 (h)=(4N1(h/2)-NT (h))/3 with error of order O(h 4)Suppose f" (x) = N(h) + a,h+ azh2 + azh + - ... The value of N½(h) using Richardson's extrapolation is: N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order 0(h^4) O N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h*2) O N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h) O N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h^2) Page 2 of 2 Back SubmitQ2. Prove that P(A^') = 1 − P(A), for any event A
- a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results. Calculate E[X2]. (b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.Suppose f"(x) = N(h) + a,h² + azh* + agh6 +.. The value of N,(h) using Richardson's extrapolation is: O N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^2) N2 (h)=2N1 (h/2)-N1 (h) with error of order 0(h^2) N2 (h)=(4N1(h/2)-N1 (h))/3 with error of order O(h^4 ) N2 (h)=2N1 (h/2)-N1 (h) with error of order O(h)5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of X is 1. fx(#) 3= 6 - a' a Var([X), (b) Var(X) > Var(X), and show the corresponding Var(X) and Var([X]), respectively, where [) represent rounding to the integer, i.e. [4.2] = 4 and (5.6] = 6.