This document discusses key properties of several probability distributions including the binomial, Poisson, and normal distributions. It explains that the binomial distribution is defined by the number of trials (n) and probability of success (p), while the Poisson distribution is defined solely by its mean. The normal distribution is then described as being defined by its mean and standard deviation. It proceeds to outline several distinguishing features of the normal distribution, including being unimodal, symmetrical, and asymptotic.

1. SUBHRAT SHARMA
CUHP13MBA85

2. • Each binomial distribution is defined by n, the number of
trials and p, the probability of success in any one trial.
• Each Poisson distribution is defined by its mean
• In the same way, each Normal distribution is identified by
two defining characteristics or parameters: its mean and
standard deviation.
• The Normal distribution has three distinguishing features:
• It is unimodal, in other words there is a single peak.
• It is symmetrical, one side is the mirror image of the other.
• It is asymptotic, that is, it tails off very gradually on each side but
the line representing the distribution never quite meets the
horizontal axis

3. • It is symmetric around the point x = μ, which is at the
same time the mode, the median and the mean of the
distribution.
• It is unimodal: its first derivative is positive
for x < μ, negative for x > μ, and zero only at x = μ.
• It has two inflection points (where the second derivative
of f is zero and changes sign), located one standard
deviation away from the mean, namely at x = μ − σ and x
= μ + σ.
• It is log-concave
• It is infinitely differentiable, indeed super smooth of order
2

4. Probability density function
Cumulative distribution
function

6. • When number of trials increase , probability distribution
tends to normal distribution .hence , majority of problems
and studies can be analysed through normal distribution
• Used in statistical quality control for setting quality
standards and to define control l