Suppose that (Xn) is a sequence of integer-valued random variab Show that weak convergence of Xn →Xo is equivalent to (d) n→∞

Q: A- Explain the following • Random Experiments. • The Variance of data. Bayes' Theorem.

A: 1. Random Experiments: A Random Experiment is an experiment, trial, or observation that can be…

Q: Σ > lan| < o, (-1, 1] For prove that 2 anx" converges uniformly on n=0 EM:

A: The proof for the convergence on [-1, 1] is shown below.

Q: 8.) Prove that lim (x₁) = 0 if and only if lin example to show that the the convergence of (Xn).…

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Q: iv) x₂ = (1 + √2/2)4n²¸

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A: Given that :- fx=1xx-1 on [2 , 4] L4=?

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A: Given that,  The functions fn and f are integrable on a,b. fn converges to f on uniformly a,b. an…

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A: Given below clear explanation

Q: Suppose that X₁, X2, ka)=P(X = _k) =1/2. Let Yn = Xn = n 2 Xi. are independent, such that, for each…

A: Chebyshev's Inequality Chebyshev's inequality guarantees that for a large class of probability…

Q: 7. Prove that a converges if kak→ 0 as k→ ∞ for some > 1. Does the result hold if a = 1?

A: The objective of the question is to prove that a sequence converges if the absolute value of its…

Q: i) Xn = ii) xn = (-1)" √n 2n²+1 √n-1 √n+1*

A: The given sequences are  (i) xn=-1nn2n2+1 (ii) xn=n-1n+1 The catchy criterion of convergence states…

Q: is it divergent, convergent or absolutely convergent?

A: We have given a series ,  ∑k=0∞ sin2k+1π2 k3k+1! Here , sin2k + 1π2 = sinkπ + π2 sin2k + 1π2  =…

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Q: A. Suppose Xn, n = 1, 2, 3, . . . is a sequence of random variables that converges in probability to…

A: Part A: Proof of Convergence in ProbabilityGiven:Xn​→PaYn​→PbWe want to…

Q: (-1)"n (xn) = п+2

A: