Let X = = Σ" X;. X₁. j=1 0 Explain why X converges in probability to 0+1*

Q: If X has an exponential distribution, show that P[(X≥t+T)|(x≥T)] = P(X≥t)

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Q: Question 2.7. Show that the following sequence is : convergent. (ii). a₁ = = 0.1, a2 = 0.12,...,a10…

A: The objective of the question is to prove that the given sequence is convergent. A sequence is said…

Q: A particle moves along the line in a random walk. That is, the particle starts at the origin…

A: It is given that  PXi=1=0.6, PXi=-1=0.4,

Q: Q3. Assuming that e = 2.71828182845... is correct to 11 decimal places, show that is a convergent to…

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Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. an = 2…

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Q: 1. A fair die is tossed 450 times. Let X denote the number of times that a number <4 is obtained. a)…

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Q: In the above problem, assume that probability of an item being defective is 0.1. Then in a random…

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Q: 3. (a) Let an max{sin 1, sin 2, sin 3,... sin n} Does {an} converge? What is its limit? Explain. =

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Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

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Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: 2. If j is the rate of simple interest for the k-th period of time, where k = 1,2,..., n, show that…

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Q: 3. Let for n € N. Is convergent? a₁ = 1, an+1 Σ n=1 = An sin an

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Q: 3 - If E is convergent, find its sum. z=1 en n(n+3)

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Q: 00 For which a does > n(In n)a converge? n=2

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Q: 10. Give an example that Xn X but Xn does not converge to X in probability.

A: 10. Let Xn=-X, for n=1,2,3,... where X~N(0,1). Now, the CDF of Xn is FXn(xn)=PXn≤xn, for xn∈ℝ and…

Q: that (An) rges in babilit to A II ntains a further subsequence that converges a.e. to X. only if…

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