Probability is primarily the measure of the
like hood of a circumstance that will occur. The higher the quantity of an
outcome the more likely is the event will occur. Dealing with random
experiments like (tossing a fair coin) probabilities can be described
numerically by the number of outcomes divided by the total number of all
Terminology of probability theory
1) Sample space: Is the aggregation of all possible
2) Sample point: Each outcome in a sample space.
Theorem (1): P (A) =1-P (A)’
Theorem (2): P (?) = 0
Theorem (3): If events A and B are such
that A ? B, then P(A) ? P(B).
Theorem (4): P (A) ? 1
Theorem (5): for any 2 events A
P (A U B) = P (a) +P (B)-P (A ? B)
Event is something which is likely to happen.
– Union event has elements that belongs to both A and B.
Intersection event contains the element which is common in A and B.
Complement event A’contains elements which is not in A
Types of random variables
Random variable: is a variable that assumes
numerical values related with the haphazard outcomes of experiment.
1) Discrete random variable: it has a
finite or infinite number of possible values.
Example: number of customers who arrive at
the bank from 8 -10 from Monday till Thursday.
2) Continuous random variable: it takes all
values interval of a real numbers.
Example: the time it takes for bulb to burn
Types of probability distributions
What is probability distribution?
It shows what is the probability of an
event to happen.
Probability shows both:
1) Simple event such as tossing a coin.
2) Complex events such as drug effect.
Probability distribution types:
*Uniform distribution: we use this
distribution when we have no prior beliefs about the distribution of
probability overcomes or when we believe probability is equally distributed
over achievable outcomes.
*Binomial distribution: It has two possible
outcomes and each probability is between 0 & 1 and they some to 1.It can
has success & failure.
We must have two conditions in order to use
1)The probability of each outcome must be
constant for all trials.
2)Triala must be independent.
*Normal distribution: It is known by its
mean and variance.
Mean, Median and mode are equal.
The normal distribution has skewness of
Normal distribution ranged from infinitely
negative to infinitely positive.
*Lognormal distribution: is a probability whose
logarithm has a normal distribution and it has infinitely negative lower bound.
It is used to calculate expected prices.