Let us suppose that the event A partitions the sample space S, i.e. AUA = S....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let us suppose that the event A partitions the sample space S, i.e. AUA = S. The indicator of an event A is the (indicator) random variable IA defined by IA(S) = = [1 if s € A ifs & A - 0 The event A occurs if and only if IA = 1. The probability distribution is PIA (0)=P(A) = 1- P(A) PIA (1) = P(A). The corresponding distribution function reads for x < 0 FLA(T) = P(A) for 0<x< 1 for x ≥ 1. Consider a probabilistic space over a set S. Show that for every event A CS and its indicator I it holds E (IA) = P(A). (An indicator is defined as IA(w) = 1 for all w E A and IA(w) = 0 for all w A.) Let us suppose that the event A partitions the sample space S, i.e. AUA = S. The indicator of an event A is the (indicator) random variable IA defined by IA(S) = = [1 if s € A ifs & A - 0 The event A occurs if and only if IA = 1. The probability distribution is PIA (0)=P(A) = 1- P(A) PIA (1) = P(A). The corresponding distribution function reads for x < 0 FLA(T) = P(A) for 0<x< 1 for x ≥ 1. Consider a probabilistic space over a set S. Show that for every event A CS and its indicator I it holds E (IA) = P(A). (An indicator is defined as IA(w) = 1 for all w E A and IA(w) = 0 for all w A.)
Expert Answer:
Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
Posted Date:
Students also viewed these accounting questions
-
Let us suppose that four guys Chico, Roberto, Bob, and Phil, eat 9 bags of corn chips. They each ate equal shares 9 / 4 bags of corn chips Later Johnny came with 11 bags and helped eat them. Now...
-
Let us suppose that a particular lecturer manages, with probability 1, to develop exams that have mean 60 and standard deviation 15. The lecturer is teaching two classes, one of size 100 and the...
-
Let X be a random variable with probability distribution where c is a constant. Determine (a) the value of c. (b) Pr(X > 1). (c) Pr(X = 3|X > 2). (d) E(X). (e) Var(X). e(x2 + 4), Pr(X=x) =I x = 0, l...
-
On December 31, 2021, L Inc. had a $1,600,000 note payable outstanding, due July 31, 2022. L borrowed the money to finance construction of a new plant. L planned to refinance the note by issuing...
-
Penguin Window Company makes and sells three product linescustom detailed windows, large standard windows, and small standard windows. The statement of operating income for the most recent period is...
-
What is the basic difference between fission and fusion?
-
A snow-cone machine at an icecream shop costs \(\$ 15,000\). The machine is expected to generate profits of \(\$ 2,500\) each year of its 10-year useful life. At the end of the 10 years, the machine...
-
The partners in River Song Company decide to liquidate the firm when the balance sheet shows the following. The partners share income and loss 5 : 3 : 2. During the process of liquidation, the...
-
A seal dives below the ice in search of fish. Its path can be modelled by where d is the depth in decameters and t the time in minutes. Use the equation above to answer questions about the seal's...
-
The January 22, 2008, press release of the Federal Open Market Committee (FOMC) states that the FOMC "decided to lower its target for the federal funds rate by 75 basis points to 3 percent." The...
-
The Security Operations Center (SOC) has noticed that a user has large amounts of data going to and coming from an external encrypted website. The SOC would like to identify the data being sent to...
-
Changes in Current Operating Assets and Liabilities-Indirect Method Victor Corporation's comparative balance sheet for current assets and liabilities was as follows: Accounts receivable Inventory...
-
In which process might mid-level executives consolidate the budget procedure by refining leadership directives as budget information is transmitted throughout the organization?
-
What does an airplane that FedEx owns and uses to deliver packages represent for FedEx?
-
Which investment strategy involves purchasing properties and renting them out to tenants for regular income?
-
how does woolworths group limited utilise Job Costing and provide a brief description of each company's revenue streams and why Job Costing would be utilised?
-
For inhomogeneous differential equations N , N^2, what kind of physical effects do you interpret this equation? and solve. dN dt The homogeneous differential equation gives the variation of a...
-
Explain the term global capital markets. This chapter primarily discusses global equity markets. What other types of financial instruments are traded in these markets? How important are global...
-
In Examples 3.9.9 and 3.9.11, find the marginal p.d.f. of Z1 = X1/X2 by first transforming to Z1 and Z2 = X1 and then integrating z2 out of the joint p.d.f.
-
For the conditions of Exercise 5, how large a random sample must be taken in order that Ep(|n p|2) 0.01 when p = 0.2?
-
Consider the situation described in Example 3.7.14. Suppose that X1 = 5 and X2 = 7 are observed. a. Compute the conditional p.d.f. of X3 given (X1, X2) = (5, 7). (You may use the result stated in...
-
Consider two alternatives, each of which will accomplish the same EPA-mandated pollution control. Using an incremental IRR analysis, determine the preferred alternative assuming MARR is 20...
-
The production department of Zunni's Manufacturing is considering two numerically controlled drill presses; one must be selected. Comparison data is shown in the table below. MARR is 10 percent/year....
-
What do you know about the mathematical value of the annual worth of a project under each of the following conditions? a. The present worth of the project is greater than 0 . b. The present worth of...
Study smarter with the SolutionInn App