Question

• Describe the various approaches used in determining probability values.
• What is the difference between discrete and continuous probability distributions? Provide your own example of each.

Answer 1

We know that,

There are 3 probability approaches as:-

1.Classical Approach:-
If an experiment has n simple outcomes, this method
would assign a probability of 1/n to each outcome. In
other words, each outcome is assumed to have an equal
probability of occurrence.
This method is also called the axiomatic approach.
Example 1: Roll of a Die
S = {1, 2, · · · , 6}
Probabilities: Each simple event has a 1/6 chance of
occurring.

2. Relative-Frequency Approach. . .
Probabilities are assigned on the basis of experimentation
or historical data.
Formally, Let A be an event of interest, and assume that
you have performed the same experiment n times so that
n is the number of times A could have occurred. Fur-
ther, let nA be the number of times that A did occur.
Now, consider the relative frequency nA/n. Then, in
this method, we “attempt” to define P(A) as:
P(A) = limn→∞(nA/n).

3. Subjective Approach. . .
In the subjective approach, we define probability as the
degree of belief that we hold in the occurrence of an
event. Thus, judgment is used as the basis for assigning
probabilities.

The basic difference between discrete probability distribution and continuous probability distribution is that discrete probability distributions takes only isolated values as 4,8,23,...etc but the continuous probability distribution can take all possible values between the interval.

For example.,

As number of students in a class can take only isolated values as 3,8,60 and not 4.5,6.2, Hence this has discrete probability distribution.

Height of students in a class can take values as 1.65m,1.72m hence this has continuous probability distribution.

Thank you.