Normal Distribution:
If X is continuous random variable and is said to follow normal distribution then the
probability density function is given by
1 x
1
f ( x)
e 2
2
2
x
0
Properties/Assu
Poisson distribution:
If X is a discrete random variable and is set to follow Poisson distribution it assume only
positive values or non negative values than the probability mass function is given by
Discrete Distributions
Binomial Distribution:
Definition: Let X be a discrete random variable it assume only Non negative values. Then the
probability mass function is defined by
P ( X x ) n Cr p r q
Bays theorem or Inverse Probability theorem:
Statement:
Let E1, E2, E3,. En are mutually exclusive events and
event A which is subset of
such that
n
UE
i
i 1
Ei
A
P
A
Ei
P( Ei ) P
n
i 1
Proof:
Probability
Introduction: Probability is a measure of how likely it is for an event to happen
Outcome: If the experiment is conducted getting result is called outcome.
Trial: the Experiment is known t
Measure of Central Tendency
Introduction: Consideration of data in to single value mostly it is at centre and it carries
important properties of data. Also known as Measure of Location or centering th
Testing of Hypothesis
Population: The aggregate of all units pertaining to a study is called population or universe.
Sample: Set of data drawn from the population is called sample. The process of sele
Probability
Introduction: Probability is a measure of how likely it is for an event to happen
Outcome: If the experiment is conducted getting result is called outcome.
Trial: the Experiment is known t
Sampling
Sample: Any part of the population is called sample. or set of data drawn from the population
is called sample.
Ex: if we want to purchase a bag of rice. The entire bag of rice is called popu
Skewness
Skewness refers to the asymmetry or lack of symmetry in the shape of a frequency
distribution. When distribution is not symmetrical (or asymmetrical) it is called a skewed
distribution. The c
Co efficient of Variation:
100 times the co efficient of dispersion based upon standard deviation is called co
efficient of variation.
Co-efficient Dispersion =
Co -effiecient of Variation =
x
100
x
Standard Deviation:
So usually denoted by the Greek letters is the square root of A.M of the square of
the deviation of the given values from their A.M.
Standard deviation for Ungrouped Data:
x
x
2
Measure of Dispersion
Literal meaning of dispersion is scatteredness. We study dispersion to have an idea of
spread about the central values of given distribution is called as Measure of Dispersion.
C
Harmonic Mean:
Harmonic mean of a number of observations is the reciprocal of the arithmetic mean of
the reciprocal of the human values
Harmonic Mean for Ungrouped data: when the date is ungrouped. Th
Geometric Mean:
Geometric mean of a set of n observations is the n th of their product. Thus, geometric
mean is denoted by G.
G.M for Ungrouped Data: when the date is ungrouped. Then Geometric mean is
Mode:
Mode of the distribution can be defined as most frequently occurring values.
Examples
1. The average height of an India (Male) is 51-611.
2. The average size of the shoes sold in a shop is 7
Mod
Median:
Median of the distribution is the value of the variable which divides it into two equal
parts
Median for ungrouped data:
If a number of observations is odd then median is the middle value afte
Simple Arithmetic Mean:
Mean is obtained by adding together all the items and by dividing this total by the no. of
items.
Mean for ungrouped data
Let X takes a values x1, x2, , xn be n observations th