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LEC07 Discrete rv, pdf, & cdf

# LEC07 Discrete rv, pdf, & cdf - A Discrete Random...

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A Discrete Random Variable, X, is a function that assigns a number to each outcome in sample space, S ex: flip a coin twice { } S HH TH HT TT = , . , r.v. X = number of heads Outcome r.v. X HH 2 TH 1 HT 1 TT 0 Possible values for r.v. X are 0, 1, and 2

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You can define many random variables to a sample space, S Flip a coin; S = { hh, th, ht, tt } Define Mapping hh th ht tt r.v. X # of heads r.v. Y # of tails r.v. Z 0 if the same 1 if different r.v. W 0 if X=Y 1 if X Y 2
Example: One Situation And Many R.V.s Customers arrive to a counter and line up for service. There is a single waiting line, , four servers, and room for 25 customers to wait on line. Observe the system for an instant. Define Mapping Possible Values r.v. W number of customers waiting r.v. N number of customers in in the system r.v. F 0 if system is not full 1 if system is full r.v. I number of idle servers 3

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Probability Distribution of a Discrete r.v. X Experiment: Flip a coin two times Sample Space: S = {hh, tt, ht, th }
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LEC07 Discrete rv, pdf, & cdf - A Discrete Random...

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