9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).
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- Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isFind the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...kSuppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)
- An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.Suppose that f(x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 24 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf will be f(x, y) = K (x² + y²) if 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 Are X and Y independent random variables? In order to answer this question, you need to find the value for K first. X and Y are not independent. X and Y are independent. cannot decide none of the other option is correct
- the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)Z is the present-value random variable for a whole life insurance of b payable at the moment of death of (x). You are given: (i) (ii) 8 = 0.05 (iii) The net single premium for this insurance is equal to Var(Z). Calculate b. x+t = 0.01 t≥0 (A) 1.36 (B) 1.68 (C) 2.00 (D) 2.32 (E) 2.64X,X, and X, is a random sample of size 3 from a population 3. with mean value u and variance o2, T, T, T, are the 3. estimators used to estimate mean value u, where T=X,+X,-X,T,= 2X,+3X, - 4X,& T, ax,+x,+x) 1 (ax,+X,+X,) (i) Are T, and T, unbiased estimators ? 1 2 (ii) Find the value of such that T, is unbiased estimator 3 for u. With this value of A is T, a consistent estimator ? (iii) 3 (iv) Which is the best estimator ?
- The discrete random variable X has Var (X) = 5 Find Var (4X – 3)Let X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution of the sample maximum X(n)In statistics, the range is computed as the difference between the minimum and maximum values Range(x) = Max(x) - Min(x) If the operatinal time of KAL CULAS graphics cards are each exponentially distribitued with a mean time of 32 months, compute the expected range of i.i.d. random variables X1, X2, X3, X4; where each random variable represents one graphics card to show your work set up all integrals correctly.
