applications of random variable

APPLICATIONS OF RANDOM DISCRETE AND Continuous

VARIBALES

Prepared By

Habib ur Rehman Chandio CE-2k14-001 Dated:16-04-2016 Civil Engineering Department Wah Engineering College(WEC)

Suppose you reach into your pocket and pull out a coin; think of one side as “heads” and the other as “tails.” You toss the coin three times. We could now define some random variables, at least informally, e.g.,

the number of heads on the first toss (which is 0 or 1),

the total number of heads (which is 0, 1, 2, or 3).

What is a random variable?

This experiment is a little hypothetical—hence the subjunctive voice. If we actually did it and

got “head tail head,” the observed value of our first random variable—the number of heads on

the first toss—would be 1; the observed value of the other random variable—the total number of

heads—would be 2.

Random variables can be:

Discrete: if it takes at most countable many values (integers).

Continuous: if it can take any real number.

If a random variable is defined over discrete sample space is called discrete random variable

DISCRETE RANDOM VARIABLE

Applications of Discrete random variable

Applications in Civil Engineering

If we want to find load on a specific point in a beam we can use discrete functions to find loading at each point on a beam.

Suppose a loading on a long, thin beam places mass only at discrete points. The loading can be described by a function that specifies the mass at each of the discrete points. Similarly, for a discrete random variable X, its distribution can be described by a function that specifies the probability at each of the possible discrete values for X.

Applications 1

Statisticians use sampling plans to either accept or reject batches or lots of construction material.

Suppose one of these sampling plans involves sampling independently 10 items from a lot of 100 items in which 12 are defective.

Application 2

Applications in Electrical Engineering

If we want to find probability of circuits accepted or not.

if number of given integrated circuit would be accepted or rejected we use discrete PMF

Application 1

If we want to find number of semiconductor wafers that need to be analyzed in order to detect a large particle of contamination in p-type or n-type material or in doping material we use random variables or discrete random variable.

Application 2

If we have number of circuit and we need the probability to test circuit to be defective and non-defective we use discrete variable distribution to find the number of defective and non-defective circuits

Application 3

For quality control: X=the number of chips examined before the first faulty one found

X(F)=1, X(SF)=2, X(SSF)=3, X(SSSF)=4, …,

X(SSSSSSSF)=8, etc.

Application 4

Applications in Business

In any business firm there is a communication system with certain number of lines to communication data and voice communication.

If we need to know the probability of how many lines are working at one time we use discrete variables.

Application 1

Other Applications

Number of airplanes taking off and landing during a given time in an airport

There are 2 PIA flights landing from Islamabad airport to King Abdul Aziz Airport at Jeddah and 2 PIA flights departing from King Abdul Aziz Airport at Jeddah every day

So 2 is a discrete number. And can be denoted as X discrete random

variable.

Application 9

Applications of continues random variable

Application in Chemical Engineering

When one conducts an investigation measuring the distances that certain make of automobile will travel over a prescribed test course on 5 liters of gasoline.

Assuming distance to be a variable measured to any degree of accuracy, and then clearly we have an infinite number of possible distances in the sample space that cannot be equated to the number of whole numbers.

Application 1

If one were to record the length of time for a chemical reaction to take place, once again the possible time intervals making up our sample space are infinite in number and uncountable. We see now that all sample spaces need not be discrete.

Application 2

Error in the reaction temperature may be defined by continues random variable with any probability density function.

Application 3

We can estimate the time at which the chemical reaction completes as we can see in this example using continues random variable.

Application 4

Application in Civil engineering

Task completion time Suppose a construction project to be

completed in 20 to 24 months and its probability is 0.05.

There are infinite sample space between 20 to 24 month.

Application 1

Clients use to estimate the price of a given construction project before and after giving bids to the public.

The Department of Energy (DOE) puts projects out. on bid and generally estimates what a reasonable bid should be. Call the estimate b. The DOE has determined that the density function of the winning (low) bid is

f(y) = 5/8b 2/5 b<y<2b, 0. elsewhere.

Application 2

The magnitude of load applied on a structural system

At any given moment in a building we cannot count the load on its roof.

We can only assume the range of load on its roof while designing

So its continuous random variable

Application 3

Application in Electrical Engineering

Engineers defines the range of the amount of current which can pass through a certain wire.

we want to know the probability of passing of certain amount of current through that wire we use continues random variable .

Application 1

We can find expected phase angle of AC circuit using continues random variable

and also we can find how the phase angle varies from original value which gives the quality of our circuit which helps electrical engineers working in quality control firms

Application 2

We can also estimate the time require for the failure of electrical component by using continues random variable and its functions.

Suppose the time till failure of an electronic component has an Exponential distribution and it is known that 10% of components have failed by 1000 hours. We use continues random variable for finding the probabilities

Application 3

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