Show that a transient DTMC eventually permanently exits any finite set with probability 1 (Use Borel-Centelli lemma)
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- Suppose that f (x) = e^-x for 0<x. Determine the following probabilities:For this Big Problem, we’re getting really really big: infinity! Sets that are infinitely bigdo interesting things. Here we’re going to experiment with some of them.(1) Give an example of a universal set U and a set A so that U is infinite and A is infiniteand A^c (complement of A)is also infinite. (2) Give an example of a universal set U and a set A so that U is infinite and A is infiniteand A^c (complement of A)is not infinite. (3) Give an example of a set A and a set B so that A is infinite and B is infinite andA ∩ B is also infinite. (4) Give an example of a set A and a set B so that A is infinite and B is infinite andA ∩ B is not infinite. (5) If A is infinite and B is infinite, can you find an example where A ∪ B is not infinite?Why or why not? (6) If A is infinite and B is infinite, can you find an example where A−B is not infinite?Why or why not? (7) An Interesting Fact is that there are different sizes of infinity. For example, if A is aninfinite set, then P(A) is even bigger.…True or false
- om/alekscgi/x/Isl.exe/1o_u-lgNslkasNw8D8A9PVVROTURTtuFljpdg)2gz8nsHUvStc_d129ID0mH9K47gzRJvgTUh5ePb8PyegUypKn82njeRdXnp4S04RDcY1Es_f56C7jBD Home | My Baker E Simplifying Fraction... E Mixed Number to I.. a Compound Interest. $ Continuously Comp.. O Future Value Annuit.. M Area of a Mail O STATISTICS Choosing an appropriate method for gathering data: Problem. Central High wants to estimate the number of seniors who plan to go to a 4-year college. Answer the following. (a) Which of the following surveys probably would best represent the entire population of seniors? O 20 seniors are randomly selected; 14 plan to go to a 4-year college. 20 honor roll students are randomly selected from the senior class; 17 plan to go to a 4-year college. O 20 chess club members are randomly selected; 13 plan to go to a 4-year college. (b) There are 600 seniors at Central High. Using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college. seniors Explanation Check 2020…3) Suppose (Ω, Σ, P) is a probability space and Ω = A1 U A2 U A3 as a disjoint union. Suppose P(A1 U A2) = a1, P(A1 U A3) = a2, where1 <= a_{1} + a_{2}2a_{1} + a_{2} <= 2a_{1} + 2a_{2} <= 2 Find P(A1), P(A2), and P(A3) in terms of a1 and a2.The joint probability function of two discrete random variables X and Y is given by Ax,y) = c(2x+y), where x and y can assume all integers such that 0< x
- i) Let X be an integrable random variable on (2, F, P) and G be a sub o-field of F. State the definition of the conditional expectation of X given G.ii) (Volterra set) Repeat the Cantor construction starting with the interval [0,1]. This time remove, in the k-iteration, an open interval of length 1/4k from the center of the remaining closed intervals to obtain SCV (4). ii-1) Draw the first 3 iterative steps of the construction of SCV (4) in detail. ii-2) Using the argument above or from Section 11.1 of the book (pages 330-332), compute the length of this Cantor-like set SCV (4), and prove that contains no intervals.Q1\ A\ Define and give an examples with its solutions for the following terms: (1) Strongly converges (2) Orthogonal set (3) Pre-Hilbert space