Probability for machine Learning(Random variable)

Random Variables:

A random variable X is a real-valued function of the elements of the sample space of a random experiment.

OR

A variable which takes the real values, depending on the outcome of a random experiments is called random variables

Types of Random Variables:

1. Discrete random variable

2. Continuous random variable

1. Discrete random variable:

A random variable which takes finite or at most countable number of value is called

Discrete random variable.

Example:

If we toss a TWO coin that sample space = S =  {HH,HT,TH,TT}

here if we take X= no of head when we toss two coins

so that X = 0,1,2 ; [because there are no head in sample space for TT = 1,                                                                                                   one head in sample space for HT,TH = 2,

                                                            two head in sample space for HH = 1]

hence we can find out probability of X=0,1,2 when we tossed two coins but we can't find out the probability of X=0.5 or X=0.3

means when we can't find out the probability for every value of X then this type of random variable is called Discrete random variable.

2. Continuous random variable:

A random variable X is said to be continuous if it takes any values in a given interval. Thus, a continuous random variable takes uncountable finite  numbers.

Example:

If we measure weight of 10,000 school students whose weight under 50kg to 60 kg

then in 10,000 students there are all types of students that someone weight is 50kg, someone weight is 50.1 kg,someone weight is 50.3kg and so on.

hence every value under 50 to 60 are covered hence this type of random variable is called Continuous random variable

when we have large number of sample space like

S={50,50.1,50.2,50.3_ _ _ _ _ _ 60}   available then it's called Continuous random variable.