Probability theory is nothing but common sense reduced to calculation -Laplace

**Probability
Distributions**

*Probability theory is nothing but common sense reduced to
calculation ***-Laplace**

The
history of random variables and how they evolved into mapping from sample space
to real numbers was a subject of interest. The modern interpretation certainly
occurred after the invention of sets and maps (1900), but as Eremenko says,
random variables were used much earlier. Mathematicians felt the need to
interpret random variables as maps. In 1812, Laplace published his book on *Theory analytique des probabilities* in
which he laid down many fundamental results in statistics. The first half of
this treatise was concerned with probability methods and problems and the
second half with statistical applications.

** **

Upon completion
of this chapter, students will be able to

• define
a random variable, discrete and continuous random variables

• define
probability mass (density) function

• determine
probability mass (density) function from cumulative distribution function

• obtain
cumulative distribution function from probability mass (density) function

• calculate
mean and variance for random variable

• identify
and apply Bernoulli and binomial distributions.

** **

The
concept of a sample space that completely describes the possible outcomes of a
random experiment has been developed in volume 2 of I year higher secondary
course.

In this
chapter, we learn about a function, called random variable defined on the
sample space of a random experiment and its probability distribution.

Tags : Mathematics , 12th Maths : UNIT 11 : Probability Distributions

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