Lec07 Discrete rv, pdf, and cdf

Lec07 Discrete rv, pdf, and cdf - 1 Discrete Random...

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Discrete Random Variables 1
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Discrete Random Variable X 2 ex: flip a coin twice r.v. X = number of heads (now each possible outcome is attached to a number) 2 1 1 0 Sample Space – set of possible outcomes Assign a numerical value for each possible { } TT HT TH HH S , , , =
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Flip coin twice experiment can lead to many random variables 3 S = { hh, th, ht, tt } Define hh th ht tt r.v. X # of heads Y # of tails Z 0 if the same 1 if different W 0 if X=Y 1 if XY
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One Queueing System can lead to many random variables 4 Customers arrive to a counter and There is a single and space for 25 waiting customers. Observe the system for an instant. Define Mapping Possibl e 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
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Probability Distribution 5 P(X=x)≥0 Adds up to 1
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Three Ways to Give Probability Distribution of the r.v. X=# heads 6 x P (X= x ) P (X= x ) 0 P(X=0) .25 1 P(X=1) .50 2 P(X=2) .25 1.
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Lec07 Discrete rv, pdf, and cdf - 1 Discrete Random...

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