Probability Definition
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
outcomes.
Terminology of probability theory
1) Sample space: Is the aggregation of all possible
outcomes.
2) Sample point: Each outcome in a sample space.
Probability theorems
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
out.
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
binomial distribution.
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
zero.
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.