Chapter 3

Chapter 3 - Randomvariables...

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CEE11 1 Random variables A random variable: from experimental outcomes to a  numerical function of the outcomes.
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CEE11 2 Random Variables -Discrete
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CEE11 Probability distribution or pmf 3
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CEE11 4 Cumulative Distribution Function
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CEE11 5 Operations on R.V.s Expectation of a RV Expectations of functions of RVs Variance
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CEE11 Expectations 6
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CEE11 7 Expectations of Functions
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CEE11 8 Variance
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CEE11 9 Property Var(aX+b)=a 2 Var(X)
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CEE11 10 Example 3.10 Consider a group of 5 potential blood donors – A,B,C,D,E – of  whom only A and B have type O+ blood. Five blood samples,  one from each individual, will be types in random order until an  O+ individual is identified. Let the r.v. Y=the no. of typings necessary to identify an O+  individual. The p.m.f of Y is
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CEE11 11 Example 3.10 (cont’d) Tabular form Line graph Probability histogram
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CEE11 12 Cumulative Distribution Function Consider Example 3.10 F(1)= F(2)= F(2.7)=
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CEE11 13 If we draw the graph, it looks like a staircase or  increasing steps, and hence such a function is also  known as a step-function.
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Chapter 3 - Randomvariables...

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