Problem 2. (Central Limit Theorem Step 1) Let X,X1,X2,� be a sequenc.pdf

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Problem 2. (Central Limit Theorem: Step 1) Let X,X1,X2, be a sequence of i.i.d. mean 0 variance 1 random variables, and set Sn=(X1++Xn)/n. Prove that EeiSn=(EeiX/n)n.

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Programming II hiding, and replacing members, Serialization, Generics, Linq ExceptionType enum You will implement this enum in Visual Studio. There are seven members: Assignment 4 - Implementing a Banking Application Due: See course shell for due date and time Check with you professor to see if you are permitted to work as a group. The members are self-explanatory. AccountType enum You will implement this enum in Visual Studio. There are three members: The application is by far the most complex system that you have attempted so far. It consists of eleven classes, two structs, one interface and two enums coupled in varying degrees of tightness. The Bank class is the main driver of the application. It has collection of Accounts and Person that is initialize appropriately in the static constructor. You will implement the entire system in Visual Studio. A short description of each type with their members is given below. You are advised to implement each type in the order that they are described. No method should have a Console. WriteLine() unless you are explicitly told to output something on the console. Each type must be in separate files. Assignment 4, Winter 2022 Assignment 4, Winter 2022 hiding, and replacing members, Serialization, Generics, ling Uses - Inheritance, Interfaces, Exceptions, EventHandlers, Collections Operator overloading, Utils class hiding, and replacing members, Serialization, Generics, Ling [The implementation for this class is given in the appendix. Create a class called UtIs and copy and 1. Time - this public class variable is of type Day Time. It adds a random value to the internal field_time and then returns it. past the statements into the appropriate part of the file] 2. Now - this public class variable is of type Day Time. It adds zero to the internal field_time You will implement the Utils class in Visual Studio. This class is comprised of three fields and and then returns it. provides two static properties. It simulates the passage of time. Each time the Time property is Methods: accessed, it increases the internal field by a random amount. It is used to time stamped all banking There are no explicitly defined methods. You do not have to code this class. Just copy the code statements from the appendix of this A short description of each dass member is given below: document. Properties: There are three properties. 1. _time - this private class variable is of type DayTime that store the time of this object. It is initialized (with argument 1_648_600_800 ) at declaration. It is mutated (changed) whenever either of the properties is accessed. 2. random - this private class variable is of type Random storing the time of this object. It is initialized (with argument 1_848_800_800) at declaration. It is mutated (changed) whenever elther of the properties is accessed. 3. ACCOUNT_TYPE - this private class variable is of type Dictionary. It serves as a lookup table to match an account type with a particular prefix, It is i.

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