Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable.

3.2

DISCRETE RANDOM VARIABLE

A random variable is called a discrete random variable if its set of posibble outcomes is countable. Probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. For example, the probability distribution of rolling a die once is as below: Outcome, x Probability, P(x) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6

The probability distribution for P(x) for a discrete random variable must satisfy two properties: 1. The values for the probabilities must be from 0 to 1; 0 ≤ ( ) ≤ 1 2. The sum for P(x) must be equal to 1; ∑ ( ) = 1

QMT200

3.2.1 FINDING MEAN AND VARIANCE Mean of X is also referred to as its “expected value”.

= ( ) Where: = ∑[ ( )]

( )=

= (

) − [ ( )]

(

)=

[

( )] = ( )

Example 1 An experiment consists of tossing two coins simultaneously. Write down the sample space. If X is the number of tails observed, determine the probability distribution of X.

QMT200

Example 2 The following table shows the probability of the number of long-distance telephone calls made in a month by residents of a sample of urban households. X 0 1 2 3 4 5 6 7 8 9 10 P(X=x) 0.02 0.05 0.08 0.11 0.14 0.22 0.28 0.04 0.03 0.02 0.01

a) Find the mean number of calls per household. b) Calculate the variance c) Find (1 < ≤ 6)

QMT200

3.2.2 MEAN AND VARIANCE OF LINEAR COMBINATIONS OF RANDOM VARIABLES Rules of Mean For any constant a and b, a) b) c) d) ( )= ( )= ( ) ( ± )= ( )± ( ) ( ± )= ( )± ( ) Rules of Variance For...

...PROBABILITY and MENDELIAN GENETICS LAB
Hypothesis: If we toss the coin(s) for many times, then we will have more chances to reach the prediction that we expect based on the principle of probability.
Results:
As for part 1: probability of the occurrence of a single event, the deviation of heads and tails of 20 tosses is zero, which means that the possibility of heads and tails is ten to ten, which means equally chances. The deviation of heads and...

...Technology & Science, Pilani
Work-Integrated Learning Programmes Division
Second Semester 2010-2011
Course Handout
Course Number
Course Title
: AAOC ZC111
: Probability and Statistics
Course E-mail address : aaoczc111@dlpd.bits-pilani.ac.in
Course Description
Probability spaces; conditional probability and independence; random variables and probability
distributions; marginal and conditional distributions; independent random...

...variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X)...

...TEM1116 Probability and Statistics
Tri1 2013/14
Chapter 1
Chapter 1: Discrete and Continuous Probability Distributions
Section 1: Probability
Contents: 1.1 1.2 1.3 1.4 1.5 Some basics of probability theory Axioms, Interpretations, and Properties of Probability Counting Techniques and Probability Conditional Probability Independence
TEM1116
1
TEM1116...

...Introduction
The word Probability derives from probity, a measure of the authority of a witness in a legal case in Europe, and often correlated with the witness's nobility. In a sense, this differs much from the modern meaning of probability, which, in contrast, is used as a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical inference.
A short history of Probability Theory............
The...

...Statistics
Chapter 5
Some Important Discrete
Probability Distributions
5-1
Chapter Goals
After completing this chapter, you should be able
to:
Interpret the mean and standard deviation for a
discrete probability distribution
Explain covariance and its application in finance
Use the binomial probability distribution to find
probabilities
Describe when to apply the binomial distribution
Use Poisson discrete...

...Probability Theory and Game of Chance
Jingjing Xu
April 24, 2012
I. INTRODUCTION
Probability theory is the mathematical foundation of statistics, and it can be applied to many areas requiring large data analysis. Curiously, that the study on probability theory has its root in parlor games and gambling. In 17th century, dice gambling was a very...

...random. What is the probability that at least one pair of shoes is obtained? 2. At a camera factory, an inspector checks 20 cameras and ﬁnds that three of them need adjustment before they can be shipped. Another employee carelessly mixes the cameras up so that no one knows which is which. Thus, the inspector must recheck the cameras one at a time until he locates all the bad ones. (a) What is the probability that no more than 17 cameras need to be rechecked? (b)...