Question: Consider a sequence (Xn)n21 of identically distributed random variables with the property that lim, xP(|X|> x) = 0. Show that max(X, X, Xn) 0

Consider a sequence (Xn)n21 of identically distributed random variables with the property

Consider a sequence (Xn)n21 of identically distributed random variables with the property that lim, xP(|X|> x) = 0. Show that max(X, X, Xn) 0 in probability. *****

Step by Step Solution

★★★★★

3.52 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

SOLUTION of if maxxil Py 10 it max Ixilxz ... View full answer

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 Mathematics Questions!

Below what temperature does the Debye equation predict ferroelectric behavior for water? Use 0 = 1.86 D and /4 0 = 1.5 10 24 cm 3 .

Consider the iteration In+1=4-(1+4k)r,+k where k ER. (a) Show that, for any kR, a 2 is a fixed point of this iteration. (b) Find the values of k for which the iteration will converge to the fixed...

In lectures we saw that if fn(z) is a sequence of functions converging uniformly to a function f(z) on some set G, then as n o, we have [ fn(z)dz [ f(z)dz. (Here is a curve contained entirely within...

A nonnegative random variable X has moments which are known to be E [X] = 1 , E [X2] = 2 , E [X3] = 5 , E [X4] = 9 , E [X5] = 14 , E [X6] = 33. (a) Show that for any nonnegative random variable, (a)...

Let $\left\{X_{n}ight\}$ be a sequence of independent and identically distributed random variables where the distribution function of $X_{n}$ is \[F_{n}(x)= \begin{cases}1-x^{-\theta} & \text {...

Let {X1, X2,...} be a sequence of independent and identically distributed random variables with PDF fX(x), and let N be an integer-valued random variable with PMF pN(n), where N and the Xi are...

15.3 Let fX1; X2; ...g be a sequence of independent and identically distributed random variables with PDF fXx, and let N be an integer-valued random variable with PMF pNn, where N and the Xi are...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of independent and identically distributed random variables from a distribution $F$ that has density $f$, characteristic function...

Let X,... be a sequence of independent and identically distributed random variables with mean 0 and variance o. Let S = X, and show that {Z,, n 1} is a martingale when Z = S - no =1

46. LetI mage be a Poisson process with rate that is independent of the sequence of independent and identically distributed random variables with mean and variance . Find

You are an audit assistant with a public accounting firm in Mayfield, Ontario. You have been assigned to audit the Accounts Receivable (AR) for Mayfield Residential Hotel (MRH), a hotel located in...

1. How would you explain Rexs leadership style in terms of one or more of the approaches discussed in the chapter? 2. What advice would you give Rex to improve his approach to leadership? 3. Could a...

5 0 Abints CSLO 1 , 2 , 5 , 6 Question 1 0 The promised coupon payments on a U . S . TIPS bond are specified in: euros. Canadian dollars. nominal terms. inflated ferms. real terms.

At December 31, 2010, Fell Corporation had a deferred tax liability of $680,000, resulting from future taxable amounts of $2,000,000 and an enacted tax rate of 34%. In May 2011, a new income tax act...

a. You are given an array of integers, where different integers may have different numbers of digits, but the total number of digits over all the integers in the array is n. Show how to sort the...

A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is normally distributed with a mean of 2 millimeters and a standard deviation of 0.1 millimeter and the...

The financial statements at the end of Four Corners Realty's first month of operations are shown below and on the shown below. Instructions By analyzing the interrelationships among the four...

Sulfur dioxide and butadienes (B3 and B2) are to be stripped with nitrogen from the liquid stream as shown in Figure so that butadiene sulfone (BS) product will contain less than 0.05 mol% SO2 and...

Find the unknown side in a right triangle with one side of 15.3 cm and the hypotenuse of 17.3 cm. Round to the nearest tenth

Consider the sequence x[n] given by x[n] = ? n u[n]. A periodic sequence x[n] is constructed from x[n] in the following way: (a) Determine the Fourier transform X(ej?) of x[n]. (b) Determine the...

In Section 11.3, we mention that a causal complex cepstrum x[n] is equivalent to the minimum-phase condition of Section 5.4. Remember that x[n] is the inverse Fourier transform of X(e j? ) as defined...

The sequence {Fn} described by F0 = 1, F1 = 1, and Fn+2 = Fn+Fn+1, if n 0, is called a Fibonacci sequence. Its terms occur naturally in many botanical species, particularly those with petals or...

Problem 1: Operations on sequences. (10 points) Consider the sequence x[n] = {1 0 -1 0 1 0}, -1 5ns 4, where the sample values outside the specified range are all zeros. And the sequence: y[n] = {-1...

Consider a sequence x[n] with descrete-time Fourier transform X(e j ). The sequence x[n] is real valued and causal, and Re{X(e j )} = 2 2 cos . Determine Jm{X(e j )}.

Consider a sequence x[n] and irs discrete-time Fourier transform X(e j ). The following is known: x[n] is real and causal, Re{X(e j )} = 5/4 cos. Determine a sequence x[n] consistent with the given...