Events

We are usually not interested in the occurrence of specific outcomes, but

rather on the occurrence of some event (i.e. whether the outcome satisfies certain conditions).

Experiment: Determine the value of a voltage waveform at time 

S = (−∞,+∞). We might be interested in the event ''voltage is negative" which corresponds to (−∞, 0).

The event occurs if and only if the outcome of the experiment is in this subset.

For this reason we define an event as a subset of S

  Experiment  E:  A  block  of  information  is  transmitted

repeatedly over a noisy channel until an error-free block arrives at the receiver.

Count the number of transmissions required. S = A = Fewer than 10 transmissions are required =

An  engineering  firm  is  hired  to  determine  if  certain waterways in Virginia are safe for shing.

Samples are taken from three rivers.

(a) List the elements of a sample space S, using the letters F for "safe to fish" and N for "not safe to fish".

(b) List the elements of S corresponding to event E that at least two of the rivers are safe for fishing.

(c)  Define  an  event  that  has  as  its  elements  the  points {FFF,NFF,FFN,NFN}.