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# Note for MATH 115A with Professor Wood at UA

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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15

Type Description Probability Function Cumulative Distribution Expected Value pf Function cdf Finite Finite discreteit can take on only finitely Probability mass function pmf F x P X lt x Random many possible values ex XOl2 or 3 fxx where fxx PX x V EX ZXPX 35 Variable In this case you can list all possible values 1nth case a histogram associated In this 0353 ll would be a Step 1 J th P X x function increasing up to 1 w1 Binomial Binomial Setting V Probability mass function pimifi FX 6 PX S x EX up Random liYou have n repeated trials of an fxx where fxx P X x V V V31 iable experiment In this case a histogram associated In thls 353 1t WOW be a Step 2 On a single trial there are two possible with P X x fumtlona moreasmg up to 1 outcomes success or failure 3iThe probability of success p is the same from trial to trial 4iThe outcome of each trial is independent Uniform Let k be the number of equally likely Probability mass function pmf O x lt x1 1 Finite outcomes 1 i E X 7 Z 3 Random Since the outcomes are countable place f x 7 X F X x E 1 1 S x S xk k 11er Variable outputs in ascending order and let i X k 1 x gt x since all probabilities are the represent the order of the output 0 615 EWher 9 k samei mm Mn gtiltgtiltgtiltgtlltgtiltgtiltgtiltgtiltgtilt Continuous Continuousif the possible values form an Probability Density function pdf FX 6 PX S x No general equation to find Random entire interval of numbers ex any positive The value of fxx 2 PX x The EXi V31 iable number value of fxx is simply the height of Pm S X S b the density curve at the value of x FX 12 FX a The value of PX x 0 Exponential Exponential random variables are Probability Density function pdf E X a Random continuous random variables and usually 0 if x lt 0 0 if x lt 0 Variable describe the waiting time between fX x left x 2 0 Fx x 17 e x 2 0 consecutive events a Uniform If X is uniform on the interval A B then Probability Density function pdf 0 x lt A B A Continuous we have a continuous uniform random 1 F x x i A A lt x lt B EX Random variable Equally likely fX x B 7 A A g x g B X B 7 A 7 7 Variable 0 elsewhere 1 x gt B

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