Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (.
Question:
(i) P(X < x) = F(x -) (the left-hand side limit).
(ii) F(x) is continuous at x if and only if P(X = x) = 0.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 37% (8 reviews)
i Let xn 0 as n and define the events An X x xn A X x Then clearly as n An a...View the full answer
Answered By
Akash Goel
I am in the teaching field since 2008 when i was enrolled myself in chartered accountants course
Since then i have an experience of teaching of class XI, XII, BCOM, MCOM, MBA, CA CPT.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
Question Posted:
Students also viewed these Statistics questions
-
Let g : ( (0, () be nondecreasing in (0, () and symmetric about 0 (g(-x) = g(x)) x ( (), and let X be a r.v, such that (g(X) < (. Then show that: P(|X| ( c) ( (g (X)/g(c) for every c > 0.
-
(i) Let X1, X2,.... Be r.v.s and let N be a r.v. taking the values 1, 2,..., all defined on the probability on the probability space ((, A, P). Define the function X as X (() = X1 (() + ... + X N (()...
-
Let X be a simple r.v. defined on (W, A ), so that Where { A j , j = 1,¦., n } is a (measurable) partition of W, and the a j , j = 1,¦., n , are assumed to be distinct. Next, let Be ay...
-
A jet is traveling westward with the sun directly overhead (the jet is on a line between the sun and the center of the Earth). How fast must the jet fly in order to keep the sun directly overhead?...
-
Which of the following is least indicative of fraudulent activity? a. Numerous cash refunds have been made to different people at the same post office box address. b. Internal auditors cannot locate...
-
How will you classify the following items in the balance sheet of a company: 1. Goodwill 2. Sundry creditors 3. Provisions for doubtful debts 4. Instalments of longterm loans due for repayment within...
-
Explain the statement that applications are solutions to information needs. Provide examples to make your point.
-
Ana used 0.5-5 percent of gross profit in determining materiality of $70,000 in her audit of XYZ Inc., a company that builds replacement engines for tractors and combines. She used the $70,000 amount...
-
Stuart Daniels estimates that he will need $ 2 2 , 0 0 0 to set up a small business in 7 years. ( a ) How much ( in $ ) must Stuart invest now at 8 % interest compounded quarterly to achieve his goal?
-
John decides to use co-ordinate geometry to check his calculations. By studying maps he concludes that the restricted airspace can be presented using a circle with equation: x + y - 18x - 14y + 117 =...
-
For n = 1, 2,¦, consider the r.v.s X n , X and Y such that | X n | £ Y , εY r < ¥ (for some r > 0), and Then show that X. >00
-
In the following expression, determine with constants a and (, so that the function F defined is the d.f. of a r.v. F(x) = 0, x ( 0, and F(x) = + (e-x2/2, x > 0.
-
Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.
-
An opinion columnist writing on bloomberg.com observes, Macroeconomists like Robert Lucas, Edward Prescott and Thomas Sargent . . . generally argued against government efforts to stabilize the...
-
Falco Oil Company began operations in 2017. During that year, Falco drilled an exploratory well on a lease located in a remote area where any oil discovered would need to be transported via a...
-
McGavin Oil Company obtained 200 Mcf of gas from Lease A and used the gas for gas injection on Lease B. The gas was valued at $12/Mcf. Assume production taxes are 5% and the royalty on Lease A is a...
-
In October 2019, Frakel Corporation drilled an exploratory well that found oil. However, the quantity of oil discovered was not commercially producible unless the price of oil went up from the...
-
Allen Petroleum drilled an exploratory well in 2018 that was still in progress at year-end. Total costs incurred by 12/31/18 were $500,000. During January 2019, drilling was continued, and additional...
-
Steel Company has two service departments, Labor and Machining, and two production departments, Fabrication and Assembly. Required (a) Determine the service department costs allocated to the two...
-
The May 2014 revenue and cost information for Houston Outfitters, Inc. follow: Sales Revenue (at standard).............. $ 540,000 Cost of Goods Sold (at standard) ..........341,000 Direct Materials...
-
Solve the following: a. 20! /17! b. 9P3 c. 7C2 Discuss.
-
Berdines Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of...
-
Winning all three Triple Crown races is considered the greatest feat of a pedigree race horse. After a successful Kentucky Derby, Corn on the Cob is a heavy favorite at 2 to 1 odds to win the...
-
If you were asked whether a large university such as Tennessee or Michigan with a large seating capacity for their football stadiums should build a new football stadium, how would you respond and...
-
J is going to receive a 30-year annuity of 8,500 and L is going to receive perpetuity of 8,500. If the appropriate interest rate is 6%, how much more is L's cash flow worth?
-
. Assume that over the past 88 years, U.S. Treasury bills had an average return of 3.5% as compared to 6.1% on long-term government bonds. What was the average risk premium on the long-term...
Study smarter with the SolutionInn App