k Suppose that Wk is a sequence of random variables. Prove that (supk≥n Wk)¯¹(a,∞) = UW(a,∞). What does this result tell us about the measurability of: Wk? supk≥n
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- Let X be a Uniform(-6,6) random variable.(a) The moment generating function of X is My(t) = A(eBt - CCt ) tD for some t in the neighbourhood of zero.Which values of the constants A, B, C, D are correct (following the same order as they occur here)? 1) 3.00, 6, -6, -12) 0.08, -6, 6,13) 0.33, 6, -6, -1 4) 3.00, -6, 6, -15) 0.336, -6,16) 0.08, 6, -6, -1Suppose that X;; i = 1,2, 3, .. n are independent random variables with a common uniform distribution over (0, 1) and Yg is distributed over (0, Yg -1) with Y, =1,k = 1,2, ..., n. Let Z = k = 1,2,3, .n R.D.R EGALA STAT 203 March 4, 2021 Show by mathematical induction induction or any other method that Zg has probability density function (-In z)*-1 fR(z) = k = 1,2,3, . n (k – 1)! Hence deduce that Zg and Y, have the same distribution (k = 1,2,3, ..n)Plzzz solve both questions
- Q2) The joint probability function of two discrete random variables X and Y is given by fx,y) = c(2x+y),where x and y can assume all integers such that 0 sIS2,0s ys3,and fx,y) = 0 otherwise. (a) Find the value of the constant c (b) Cov (X, Y), (c) p.Advanced Math (a) Suppose X, Y, Z:2R are three discrete random variables. Prove that (Px py) Pz Px (py pz). This says that the convolution product is associative. (b) Suppose X and Y are discrete random variables with X Bin(4, ) and Y ~ Bin(5, ). Using the definition of convolution, calculate px + py. (Vandermonde's identity may be useful here.) Can Kou Gnd y quick way of deing this calculation by thinking of Y and Y ax indenendent random#5