Question

Define and give examples of each of the following scenarios.

1) discrete

2) continuous

3) mixed

4) dynamic

5) stochastic

Answer 1

(1) Discrete data is the data that can take only certain values. Example: Number of students in a class:, because it can take only integer values. Discrete distribution describes the probabilities of a discrete random variable. Suppose we tossa coin. The distribution of number of Heads is a discrete distribution.

(2) Continuous data is the data that can take any value within an interval. Example: Height of a person, because it can be any value within the range of human heights. Continuous distribution describes the probabilities of a continuous random variable. For example Uniform Distribution gives equal probability for all values of the random variable between a and b.

(3) Mixed distribution is defined as the probability distribution of the random variable which is invented from the compilation of other random variables.

Example: Let X be a continuous variable.f(x) in the interval: 0 x 1.

Then the variable Y defined by:

Y = g(x) = x for 0 < X 1/2

               = 1/2 for X > 1/2.

Here g(x) is a mixed distribution.

(4) Dynamic data is the one that changes over time as new information becomes available. Time series analysis is an example of dynamic data analysis.

(5) Stochastic Process is a random process evolving with time. It is a family of random variables X_s indexed by a parameter , where belongs to some index set .   Markov chain is an example of Stochastic Process, which describes a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.