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RANDOM VARIABLES

Random VariablesExamples of continuous random variables: length, pressure, temperature, time, weight

Examples of discrete random variables:Number of bulldozer that remain operating after 6 months, the opening and closing of highway routesDecide whether a discrete or continuous random variable is the best model for each of the following variables: The time until a projectile returns to earth. (b) The number of times a transistor in a computer memory changes state in one operation.(c) The volume of gasoline that is lost to evaporation during the lling of a gas tank. (d) The outside diameter of a machined shaft. (e) The number of cracks exceeding one-half inch in 10 miles of an interstate highway. (f) The weight of an injection-molded plastic part. (g) The number of molecules in a sample of gas. (h) The concentration of output from a reactor. (i) The current in an electronic circuit.For each of the following exercises, determine the range (possible values) of the random variable. 3-1. The random variable is the number of nonconforming solder connections on a printed circuit board with 1000 connections. 3-2. In a voice communication system with 50 lines, the random variable is the number of lines in use at a particular time. 3-3. An electronic scale that displays weights to the nearest pound is used to weigh packages. The display shows only ve digits. Any weight greater than the display can indicate is shown as 99999. The random variable is the displayed weight. 3-4. A batch of 500 machined parts contains 10 that do not conform to customer requirements. The random variable is the number of parts in a sample of ve parts that do not conform to customer requirements. 3-5. A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected

outcomeabcdefx001.51.523x21012f(x)1/82/82/82/81/8E4A contractor is planning the acquisition of bulldozer for a new project. He estimated that there is a 50% chance that each bulldozer can remain operational after 6 months. He purchased 3 bulldozers.

Using X as the random variable whose values represent the number of operating bulldozer after 6 months,, the events of interest should be mapped into the real line. Thus X=0 X=1 X=2 X=3 now represent the corresponding events of interest.

Find the probability mass function ( probability distribution) of X

Determine the cumulative distribution function.Mean and Variance of a Discrete Random VariableDetermine the mean and variance of the random variable in E1

Determine the mean , variance , standard deviation, and coefficient of variation of the random variables in E4