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Running Head: DECISION MAKINGDecision MakingName of the StudentName of the UniversityAuthor Note

1DECISION MAKINGTable of ContentsANSWER NUMBER 1...................................................................................................................2ANSWER NUMBER 2...................................................................................................................5ANSWER NUMBER 3...................................................................................................................6REFERENCES................................................................................................................................9

2DECISION MAKINGANSWER NUMBER 1a)In certain situations, real numbers are attached along with the elementary events that canbe obtained by performing a random experiment. The elementary events that can be obtained byconducting a random experiment is known as the sample space. As an example, tossing of a coincan be considered. Let the number 1 be assigned with the appearance of a tail and 0 be assignedwith the appearance of head. This is how a function is defined on a sample space. A (real valued)function defined on the sample space is known as therandom variableor astochastic variable.To each value of a random variable X, there corresponds a definite probability.Random variable can be classified into two types–discrete random variablesandcontinuous random variables(Miller & Miller, 2015).A random variable, which takes a finite number of values or a countably infinite numberof values, is known as adiscrete random variable. The number of misprints in a page of book isan example of a discrete random variable.A random variable is said to be continuous if it assumes uncountably infinite number ofvalues. For example, the waiting time in a bus stop for the arrival of a bus is a continuousrandom variable.b)The term expected value of a random variable means the value predicted for therespective random variable. It is denoted by E(X) and serves as a measure of central tendency ofthe probability distribution of X. It is usually defines as the sum of the values of the random

3DECISION MAKINGvariables multiplied by their respective probabilities. If X assumes the values x1, x2, ...., xkwithrespective probabilities p1, p2, ...., pk, where∑i=1kxipi=1, thenE(X)=∑i=1kxipi, provided it is finite.For example, let a coin be tossed continuously till the first head appears. The number ofthrows needed to get the first head is a random variable denoted by X, taking the values 1, 2, 3,....ad inf. Further, if the coin is unbiased, the probability of getting a head in a throw is 1/2 andof getting a tail is 1/2. Hence,p[X=k]=(12)k−1∗12,for the throws are made independently of each other and x = k if and only if, a head is obtainedin the kththrow but in none of the earlier throws.The mathematical expression of X is, therefore,E[X]=∑k=1∞k(12)k−1∗12=16[1+2(12)+3(12)2+...]=12(1−12)−2=4.Thus, on an average, 4 throws will be needed to get the first head.c)The expected values of the variables, their respective probabilities and cumulativeprobabilities have been calculated and given in the following table.

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