Discrete Random Variables (2)

Discrete Random Variables (2) - Discrete Random Variables...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Sections 3.2 and 3.3 Page 1 Discrete Random Variables Sections 3.2 and 3.3 Numeric Random Variables h The numerical outcome of a random circumstance is called a random variable . h Random variables are variable because they keep changing values. h Random variables are random because we don’t know the next value the random variable will assume. h Although we don’t know the next value, we do know the overall pattern of the values assumed by a random variable over many repetitions. h The pattern of the values of a random variable over many repetitions is called the distribution of the random variable . 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0 1 2 3 4 5 6 Relative Frequency Ounces Number of Active Pumps 16.0 16.2 16.4
Background image of page 1

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

View Full DocumentRight Arrow Icon
Sections 3.2 and 3.3 Page 2 Notation h We will use capital letters from the end of the alphabet to represent a random variable. o Usually X or Y h The corresponding lower case letter will represent a particular value of the random variable. o P(Y = y) is the probability that the random variable Y is equal to the value y. h Discrete and Continuous Random Variables h A continuous random variable can take any value in an interval of the real number line. o Usually measurements h A discrete random variable can take one of a countable list of distinct values. o Usually counts Discrete or continuous? h Time until a projectile returns to earth. h The number of times a transistor in computer memory changes state in one operation. h The volume of gasoline that is lost to evaporation during the filling of a gas tank. h The outside diameter of a machined shaft. h Other Examples
Background image of page 2
Sections 3.2 and 3.3 Page 3 Example. A small airport in New Zealand is interested in the number of late aircraft arrivals per day. Every day for a year it counts the daily number of late arrivals. Let random variable Y = Number of aircraft in one day that arrive late. Y 0 1 2 3 4 P(Y=y) 0.118 0.186 0.296 0.260 0.140 h What is the probability that on any randomly chosen day that 3 aircraft are late? h What is the chance that on any randomly chosen day that more than 3 aircraft are late? Example. An assembly consists of three mechanical components. Suppose that the probabilities that the first, second, and third components meet specifications are 0.90, 0.95 and 0.99 respectively. Assume the components are independent. Let S i = the event that a component is within specification. Possible Outcomes for One assembly g G g ± g ² g G g ± ³ g ² ³ g G ³ g ± g ² ³ g G ³ g ± ³ g ² g G ³ g ± g ² g G g ± ³ g ² g G g ± g ² ³ g G ³ g ± ³ g ² ³ 0.84645 0.00045 0.00095 0.09405 0.04455 0.00855 Let Y = Number of components within specification in a randomly chosen assembly Y 0 1 2 3 P(Y=y) 0.00005 0.00635 0.14715 0.84645
Background image of page 3

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

View Full DocumentRight Arrow Icon
Sections 3.2 and 3.3 Page 4 Probability Function p(y) = P(Y = y) Note: Probability Function for a Discrete Random Variable can be expressed as a table or graph and sometimes as a formula. Cumulative Distribution Function
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 18

Discrete Random Variables (2) - Discrete Random Variables...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online