We consider a sequence (X^)^-1 of independent random variables such that P(X=1)=1- P(Xn = −1) = Pn. n For all n < N, let So = 0 and S₁ == > X₂. We also consider the filtration (F)-1 given by i=1 Fn=σ(X1,..., Xn). (d) Is there a choice of the values of pn (n> 1) such that (S2) 0 is a martingale ? (e) Consider the process (V)-1 defined by n ΔΥΠ Vn == = ASn Prove that (n)=1 is previsible. Yn - Yn-1 Sn - Sn-1

Q: Suppose the random variable XX is uniform on the interval from 20 to 70, so X∼U(20,70).X∼U(20,70).…

A: As per bartleby guideline expert have to answer first three subparts only dear student please upload…

Q: Let i_t denote the effective annual return achieved on an equity fund achieved between time (t -1)…

A: Given that an investor has a liability of £10,000 payable at time 15.Mean Sigma

Q: let k be a random variable that takes with equal prob 1/(2n+1), the values in integer the interval…

A: Let X be a random variable that takes on integer values in the interval [-n, n] with equal…

Q: If the probability of occurrence of an event (probability of success) in a single trial of a…

A:

Q: A random variable W has range RW = {1, 2, 3, . . . } and the probability mass function given by…

A: The provided information is as follows:The  is a random variable having a range .The probability…

Q: Suppose that X₁, the number of particles emitted in t hours from a radio - active source has a…

A:

Q: If x is a random variable (3,x-bn), find the smallest value for n so that it achieves 0.8 <(1 2 p(x)…

A: If a random variable X follows binomial distribution. X~Bx, n, p=13 and PX≥1&gt;0.8 We need to find…

Q: Let X be a Gaussian random variable (0,1). Let M = e^(5*X) be a derived random variable. What is…

A: Let  X be a Gaussian random variable with mean 0 and variance 1. We know that its probability…

Q: At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will…

A: Since you’ve posted a question with multiple sub-parts, we will solve the first 3 sub-parts and…

Q: and sen) halsaf Show that for random samples of size n from an exponential population with the…

A:

Q: Let X be a random variable with p.d.f. 4k 1< x<10 f (x) =< find k. O.W

A:

Q: Uniform distribution Unif (-8.0] having paf fix;o) = 0 - xE l-8. e] and zero elsewhere. hat is the…

A:

Q: Suppose the time it takes Alex to do this exam is exponentially distributed with parameter 3 per…

A: Introduction to Exponential distribution: A random variable X is said to have a exponential…

Q: Compute the moment generating function (mgf) of a geometric random variable, where the pmf is P(k) =…

A:

Q: Let N(m, \sigma^2) be a Gaussian distribution with mean m and variance \sigma^2. Calculate KL(N(0,…

A:

Q: Suppose that the random variable X follows a beta distribution with alpha=1 and beta=3, Beta(1,3)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Ex//let xa random variable with pm f p X=xN N , x=1,2,.., N and let Y=a+bx where a, bER find Ey and…

A:

Q: Suppose k is a binomial random variable with parameters n and p and let x=(k-np)//sqrt(npq) where…

A: Given:To prove:

Q: pose that Y1,Y2 are independent identically distributed (iid) random variables form a random sample…

A: y1 0.04304550 y2 0.50263474 f(x)=θe-θx ; x≥0 1) Read the data into R x&lt;- c(0.04304550,…

Q: The probability of an event depends on the random variable X and can be expressed by the following…

A: Given:P(A|x)=1-e-kx ;x≥0 where k&gt;0Given that X is a normally distributed random variable with…

Q: If P(B) = ³/ and P(A'^B)= 1, for two events A and B, find P(A/B).

A:

Q: Page 327, 5.1.7.* Let X₁, ...,Xn be iid random variables with common pdf f(x) exp{-(x-20)}, x > 20,-…

A:

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: The probabilities of a random variable X are given as when x, =, Plz) =} 1 2 -1 1 P(x,) = 2 and X2…

A:

Q: Let X,Y be two random variables and take values in {0,1} and whose joint distribution is given by: (…

A: First, we need to calculate the expected values of X, Y, X^2, and Y^2. The expected value of a…

Q: Derive the MGF for an exponential random variable X ~ exp(A) (try the Kernel trick!) O eta t-入…

A:

Q: Suppose the inter-arrival time of people using the elevator can be modeled as X ~ Exp(1/6) (in…

A: From the given information, It has been given that X is the random variable that shows inter-arrival…

Q: You have two random variables M and N where the joint pdf is given by  f_M,N(m,n) = b if m + n >=2,…

A: The region in which f=b is shown in figure:  f=0 for other values of (m,n)

Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)=• find k. O.w

A: The p.d.f of X is given below: fx=kx-2   1&lt;x&lt;∞0          ow

Q: random variable

A:

Q: Let X be à discrete random variable with pmf fax² p(¹) = | e z=0,1,2,3,4 otherwise à) If p(0) = .14,…

A: Here , we have given a pmf which is describes in the question.

Q: The discrete random variable T has the p.m.f   P (T=m)=2^m -1 / 3^m , m=0,1,...,m,... Show that…

A: