Lecture 1 Experiments, Models and Probabilities

Outline

Definition An outcome of an experiment is any possible observation of that experiment. The sample space of an experiment is a set of all possible outcomes. An event is a set of outcomes of an experiment. An event space is a set of events.

Telephone Usage Question: Determine the probability of a long call.

Conditional Probability

Resistor Variability (1)

Resistor Variability(2)

Traffic Lights

Permutations Shuffle the deck and choose three cards in order. How many outcomes are there? – 52 x 51 x 50

Choose k objects out of n

Resistor Variability(2)

Transmission of Information

Transmission of Data Packets

Definitions For n trials of a subexperiment with sample space S={s 0,,,,s m-1 }, we want to find the number observations sequences in which s 0 appears n 0 times, s 1 appears n 1 times, and so on.

Chip Fabrication How many elements are in the entire set of possible sequences? n 0 =2 n 1 =2 n 2 =3 n 3 =3

Multinomial Coefficient

Example

Chip Fabrication (3)

Reliability

Redundant Parts

Matlab

factorial(n)

nchoosek(n,k)

Flip a Fair Coin 4 Times

ceil()

Execution

Plot the histogram

Packets

Matlab Code

# of packets in simulation n=100 n=10000n=100000