Question

Explain the difference between continuous random variables and discrete random variables. please give examples!

Answer 1

Solution :-

A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

A discrete variable is a variable whose value is obtained by counting.

Examples:     number of students present

                                    number of red marbles in a jar

                                    number of heads when flipping three coins

                                    students’ grade level

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A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements.

A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values, and is represented by the area under a curve (in advanced mathematics, this is known as an integral). The probability of observing any single value is equal to 0, since the number of values which may be assumed by the random variable is infinite.

A continuous variable is a variable whose value is obtained by measuring.

Examples: height of students in class

                        weight of students in class

                        time it takes to get to school

                        distance traveled between classes