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A probability is a measure of likelihood that a future event will occur; it can assume a value between 0 and 1, inclusive.

A sample space is the collection of all possible outcomes for an experiment.
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An experiment is any process that generates well-defined outcomes.

An event is a possible outcome of an experiment.
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Relative frequencyis defined as the number of times an event occurs divided by the total number of times the experiment is performed.


Subjective probability reflects feelings or opinions concerning the likelihood that a particular outcome will occur.

Two events are independent if the occurrence of one in no way influences the occurrence of the other.

The complement of any event is the collection of outcomes that are not contained in that event.

A list of events is collectively exhaustive if every possible event that can occur is on the list.

Events are mutually exclusive if the occurrence of one precludes the occurrence of any other.
Addition rule of probability is stated as:
For events that are not mutually exclusive:
P(A or B) = P(B) – P(A and B).
For mutually exclusive events:
P(A or B) = P(A) + P(B).
Multiplication rule of probability is stated as:
For events that are independent:
P(A and B) = P(A) X P(B).
For events that are dependent:
P(A/B) = (P(A and B))/(P(B)).


A random variable has a numerical value that varies from case to case on a random basis.

A discrete random variable is a variable that can assume only values from a predetermined set.

A probability distribution is a listing of the possible values that a random variable can assume along with their probability.

The expected value of a discrete random variable is the average value that the random variable assumes over a large number of observations.

The binomial distribution is a discrete probability distribution involving the likelihood of X successes in n trials of a binomial experiment.

Essential characteristics of the binomial distribution are
There are n identical trials that lead to one of two outcomes: success or failure.
The probability of each outcome remains constant from trial to trial. The probability of one of these outcomes, called success designated p and the other, failure designated q = 1 – p.
The trials are independent.
A combination (symbolize C_x^n) represents the number of possible ways of choosing X things out of n things when the order of choosing is not important.

The hypergeometric distribution is used to model finite-population situations where sampling is done without replacement and were the
probability of a certain number of successes is to be calculated.

The poison distribution is used to model situation where there are random arrivals of events per unit of space or time, and where the probability of a specific number of successes is to be determine.
Essentials characteristics of the poisson distribution are:
The mean and the variance of poisson distribution are equal
The probability of an occurrence is the same throughout the time interval or space unit.
The probability of more than one occurrence in an interval is approximately zero.
The number of occurrences in any interval is independent of the number of occurrences in other interval.

A continuous random variable is measured on a numerical scale. Each observation of the random variable can assume any value within some specified range.

The uniform distribution describes a random variable that is as likely to occur in one segment of a given size within a specified range as another.

The normal distribution is a continuous distribution that has a bell-like shape and is determined by its mean and standard deviation.
The normal distribution has a bell-like shape and is symmetrical about its mean.
Knowledge of the mean and standard deviation is necessary to identify a specific normal distribution.
Each combination of mean and standard deviation specify a unique normal distribution.
The normal distribution extends indefinitely in either direction from the mean.
The normal distribution is measured on a continuous scale, and the probability of obtaining a precise value is zero.
The total area under the curve is equal to 1.0 100%. 50% percent of the area is above the mean, and 50% is below the mean.
The probability that a random variable will have a value between any two points is equal to the area under the curve between those two points. This area can be determined using either calculus or the standard normal table.

The standard normal distribution has a mean equal to 0 (zero) and standard deviation equal to 1 (one).
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The Z-value is a measure of the number of standard deviation between the mean or center of a normal curve and the value of interest.

It is calculated as Z (X- μ)/σ
Z=number of standard deviation from mean
X=value of interest
μ=mean of distribution
σ=standard deviation of distribution

Chebysev’s distribution or Chebysev’s theory
Regardless of how data value are distributed, at least (1- 1⁄k^2 ) of the values will lie within k standard deviations of the mean (for k ≥1)
The normal distribution provides a close approximation to the binomial distribution when n is large and p is close to 0.5. As a rule of thumb, this approximation is appropriate when np>5 and n(1-p)>5.
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