lec2class

# lec2class - CHAPTER 2 Probability Sample Space 2.1 A random...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 2: Probability Sample Space: 2.1 A random experiment is an experiment in which the outcome varies in an unpredictable fashion when the experiment is repeated under the same conditions. Examples • Experiment E 1 : Toss a coin three times and note the sequence of heads and tails. • Experiment E 2 : Toss a coin three times and note the number of heads • Experiment E 3 : 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. • Experiment E 4 : Measure the lifetime of a given computer memory chip in a specified environment. Since random experiments do not consistently yield the same result, it is necessary to determine what the set of possible results can be. The sample space S of a random experiment is defined as the set of all possible outcomes. Note: When we perform a random experiment, one and only one outcome occurs. The samples spaces corresponding to the experiments in the last Example are given below: • Experiment E 1 : Toss a coin three times and note the sequence of heads and tails. • Experiment E 2 : Toss a coin three times and note the number of heads • Experiment E 3 : 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. • Experiment E 4 : Measure the lifetime of a given computer memory chip in a specified environment. Random experiments involving the same experimental procedure may have different sample spaces as shown by Experiments E 1 and E 2 . 1 A tree diagram: Example: The three balls numbered 1 to 3 in an urn are drawn at random one at a time until the urn is empty. The sequence of the ball numbers is noted. Find the sample space. Events: 2.2 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). Example: Experiment: Determine the value of a voltage waveform at time t 1 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 Example: Experiment E 3 : 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 3 = A = Fewer than 10 transmissions are required = Ex. 10 on p. 30: An engineering firm is hired to determine if certain waterways in Virginia are safe for fishing. Samples are taken from three rivers....
View Full Document

## This note was uploaded on 12/16/2011 for the course CS cs102 taught by Professor Rsharma during the Spring '11 term at IIT Kanpur.

### Page1 / 16

lec2class - CHAPTER 2 Probability Sample Space 2.1 A random...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online