Let (N, F,P) be a probability space. Let A = (An)nƐN be a countable partitionof N, and let G = o(A). Let X be a real and integrable random variable. ShowthatE[X|G] = _E[X| A„] 1An•nƐN

Given: Here the given are Consider Ω,F,ℙ be a probability space and Α=(An)n∈ℕ be a countable…

Answered: Let (N, F, P) be a probability space.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Let f(x) = x for 0 < x < 1. Is f(x) a legitimate probability distribution function (pdf) for a continuous random variable? No, the area under f(x) is not 1 (it is greater than 1). Yes, all criteria for a pdf are satisfied. No, the area under f(x) is not 1 (it it less than 1). No, f(x) is not non-negative.
9 -Probability density function for a continuous random number For 1 <x <3, it is equal to f (x) = (6/32) x +2/16. for other cases, f (x) = 0. Find the cumulative probability function F (x <1 and x = 1) of the continuous probability division. A)1/5 B)0 C)1/2 D)1/4 TO)3/4
1
Let X be a continuous random variable with cdf F(x). Show that E(I(X < x)) = F(r) where I is the indicator function (1 if X
Let X be a random variable with the following probability density function: f (x) = (1 – a2), –1 < x < 1 4 and f (x) = 0 otherwise. Give the integrals for the following: a) The mean b) The variance c) P[ -0.75 < X < 0.5 ]. d) the CDF
A shop receives a shipment of 1000 lamps. The probability that any individual lamp is defective is 0.2%. Assume the defectiveness is independent of cach lamp. Let X be the number of defective lamps in the batch of 1000. What is the probability mass function of X? O P(X = k) = (00) 0.002* (1 – 0.002)1000 , k = 0,1, 2, ..., 1000 O P(X = k) = 0.002* (1 – 0.002)1000–&, k = 0, 1, 2, .….., 1000 O P(X = k) = (1000) 0.002* (1 – 0.002)1000 , k = 1, 2, ..., 1000 O P(X = k) = (00)0.002100- (1 – 0.002)*, k = 0, 1, 2, ..., 1000
The probability that none of the three bulbs in a set of traffic lights will have to be replaced during the first 1200 hours of operation if the lifetime X of a bulb (in thousands of hours) is a random variable with probability density function f(x) = 6[0.25-(x-1.5)2] when 1 ≤ x ≤ 2 and f(x) = 0 otherwise is
The probability density function of the discrete random variable x; x = 1,2,3 8 - f(x dd(other cases) olarak tanımla is defined as. Calculate the expected value of x accordingly. O A) 1/6 OB) 2 O C) 7/3 OD) 5/2 OE) 3/5
Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function c) Let Ô₁ = X₁+2X₂+2X3-X4 4 f(x; 0) = 0xe xc! for x = 0,1,2,... elsewhere ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which one of the two estimators is more efficient?
Do not need matlab
Let X be a continuous random variable with probability density function xe-X x20 fxlx) = 0 otherwise The value of a Select one: a. can be any positive real number b. must be 1 c. can be any real number d. can be any positive integer
Let X be a finite random variable with the expected value u = µx. Choose a correct variant below to fill in the blank in order to obtain a valid formula: Var(X) Select one: a. E(X²) b. E(X) c. [E(X)]²

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Let (N, F, P) be a probability space. Let A = (An)nɛN be a countable partition of N, and let G = o(A). Let X be a real and integrable random variable. Show that E[X|G] = £E[X|A„] 1Am• nƐN