Pstat160B Manufacturing management example Solution
Winter 2009
The exponential property of the inter-arrival of the demand and production give the Markov property, provided that the state space encode the necessary information: quantity in stock and if t
Pstat160B Manufacturing management example
Winter 2010
A machine, when turned on, produce items at a rhythm of a Poisson process with rate per hours. Demand occur according to a Poisson process with rate per hours. The stock capacity is of 4 items, and so
Spring 2010
Pstat160b
Handout #4
Residual lifetime and hazard rate
Let X be a non-negative continuous random variable. It will be interpreted as a random time (lifetime for instance), with pdf f , cdf F , andtail probability orcomplementary cdf or surviva
Spring 2010
Pstat160b
H-O #3
Exponential Distribution summary
Notation: We denote the exponential distribution with parameter > 0 by E (). Interpretation: Exponential random variables will often be interpreted as the time an event occur, or as a random cl
Pstat160b Syllabus
Classes: MWF 1:00-1:50 p.m. Room:
Spring 2010
North Hall 1109
Instructor: Dr. Guillaume Bonnet Oce: South Hall 5503 Oce Phone: 893-8088 Email: [email protected] Oce Hours: M, 11:00-11:30 a.m. & 4:15-5:00 p.m. W: 11:00-12:00 a.m If yo
Pstat160b
Spring 2010
Main formulas
Discrete distributions name pX ( k ) =
N1 N2 k nk N1 +N2 n
expected value 0 k N1 n N2 k n
N1 n N1 +N2
variance
Hypergeometric (N1 , N2 , n) i select n Binomial (n, p) Poisson () Geometric (p) Negative Binomial (r, p)
k1
Spring 2010
Pstat160b
Example
Random demand problem
Suppose the demand X for some product is random with exponential distribution with parameter (say some fruits in tons). The manager of a store orders K units (can be continuous) for $ 2 per units (could
Spring 2010
Pstat160b
H-O #5
Simulation of Continuous Random Variables
The starting point of all simulations methods is uniform U (0, 1) random variable. Those are obtained from (pseudo) random number generator, which we assume are available to us. Note t
Spring 2010
Pstat160b
H-O #1
Continuous Distribution summary
Recall that if X is a continuous random variable, P (X = x) = 0, for any number x. Cumulative Distribution Function The C.d.f (cumulative distribution function) of a continuous random variable X
Spring 2010
Pstat160b
Handout
Bayesian Statistics example: Binomial/Beta conjugate prior
Set-up: Binomial trials (say coin tosses) where the probability of success p is unknown. This is a typical example in statistics where one would want to estimate p, b