Question: Consider a sequence {X n ,n = 1, 2, 3,} such that Show that Xn = n 0 with probability n2 with probability 1 1

Consider a sequence {Xn,n = 1, 2, 3,⋯} such thatXn = n 0 with probability n2 with probability 1 1 n

Show thata. Xn 0. L" b. Xn0, for r < 2. c. Xn does not converge to 0 in the rth mean for any r > 2. a.s. d. Xn 0.

Xn = n 0 with probability n2 with probability 1 1 n

Step by Step Solution

★★★★★

3.45 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Introduction To Probability Statistics Questions!

Q:

Consider a sequence of IID random variables, Xn n = 1, 2, 3 each with CDF FXn (x) FX (x) 1 Q (x / ). This sequence clearly converges in distribution since FXn (x) is equal to FX (x) for all n. Show...

Q:

A sequence of zero mean unit variance independent random variables, Xn, n = 0, 1, 2, , N 1 are input to a filter that produces an output sequence according to Yn = (Xn + Xn 1)/ 2, for . For n = 0,...

Q:

(x, y) = (0,0) (x, y) = (0,0) Given f(x, y) = x2 Determine (a) whether f(x, y) is continuous at (0,0); (b) whether fx (0,0) and fy (0,0) exist, and their values, if they do; (c) whether f(x, y) is...

Q:

Need help here. 1 For a stochastic process X,, with time set / and state space S, define the terms: (i) stationary (ii) weakly stationary (iii) increment (iv) Markov property. 2 A moving average...

Q:

Consider the following probability distribution: a. Find , 2 and . b. Find the sampling distribution of x for random samples of n = 2 measurements from this distribution by listing all possible...

Q:

please help me solve these questions, the teacher included the final answer in the screenshots but I want the steps for it so I can understand how they got the final answer ( that's all screenshot so...

Q:

\f\f\f\f\f\f\f\f\f\fSequences, Mathematical Induction and Recursion 1 5.1 Sequences 2 Sequences Sequences represent ordered lists of elements. A sequence is defined as a function from a subset of N...

Q:

Recursion (Please solve on Java netbeans 8.1 or 8.2) I solve parts of this problem ( which is between 1-5) Solve from 6 Create the following methods and test them using a TestRecursion class 1. A...

Q:

Consider a jewelry that only sells diamond rings and operates as follows. Each week, the store is open from Monday-Friday. The weekly (5-day) demand is random, and has distribution Pr(D=d) = 1/6...

Q:

5. (Unary acceptance) A Turing machine M accepts a unary string if there exists a string x E {1}* such that M accepts on input x. Consider the problem of determining whether (the encoding of) a TM M...

Q:

Assume the following: Loan Type Principal Amount APR Repayment Schedule (years) Payment Frequency (#) What is the interest paid in year 7? Level-principal $395,216 7.1% 17 he Annual

Q:

16) From the latest financials for my company, I extracted the following information for my boss: Total Assets: $1,200,000 Total Equity: $ 650,000 Total Sales: $6,000,000 Net Profit: $ 480,000 From...

Q:

Dari Inc. guaranteed the debt of a related party. In December, Dari learned that it is probable it will be required to pay between $150,000 and $200,000 within the next six months in satisfaction of...

Q:

How do you believe ones basic philosophy of human nature affects ones approach to leadership?

Q:

With reference to Exercise 4.38, find the variance of the probability distribution using (a) the formula that defines \(\sigma^{2}\); (b) the computing formula for \(\sigma^{2}\); (c) the special...

Q:

As can easily be verified by means of the formula for the binomial distribution (or by listing all 16 possibilities), the probabilities of getting \(0,1,2,3\), or 4 red cards in four draws from a...

Q:

Find the mean and the variance of the uniform probability distribution given by \[f(x)=\frac{1}{n} \quad \text { for } x=1,2,3, \ldots, n\] The sum of the first \(n\) positive integers is \(n(n+1) /...

Q:

Can someone explain how we got the 5000 as the ending inventory?

Q:

Pintura Residencial se encuentra conciliando su Cesanta del Estado y tiene saldo negativo en su cuenta de Pasivo Nmina. Qu 2 informes comparara para aislar la discrepancia?

Q:

Do not copy from chegg!!! show all steps and provide answer 15 k/ft 15 ft. k 15 ft. k C A B 6' 10 6 1. Draw shear force and moment diagrams for the beam above