Random Variable Example with Solutions
Here are some of the solved examples on Random variable. Learn random variables by practicing these solved examples.
Example 1
Find the mean value for the continuous random variable, f(x) = x2, 1 ≤ x ≤ 3
Solution:
Given,
f(x) = x2
1 ≤ x ≤ 3
E(x) = ∫31 x.f(x)dx
E(x) = ∫31 x.x2.dx
E(x) = ∫31 x3.dx
E(x) = [x4/4]31
E(x) = 1/4{34– 14} = 1/4{81 – 1}
E(x) = 1/4{80} = 20
Example 2
Find the mean value for the continuous random variable, f(x) = ex, 1 ≤ x ≤ 3
Solution:
Given,
f(x) = ex
1 ≤ x ≤ 3
E(x) = ∫31 x.f(x)dx
E(x) = ∫31 x.ex.dx
E(x) = [x.ex – ex]31
E(x) = [ex(x – 1)]31
E(x) = e3(2) – e(0)
E(x) = 2e3
Random Variables
A random variable in statistics is a function that assigns a real value to an outcome in the sample space of a random experiment. For example: if you roll a die, you can assign a number to each possible outcome.
Random variables can have specific values or any value in a range.
There are two basic types of random variables,
- Discrete Random Variables
- Continuous Random Variables
In this article, we will learn about random variable statistics, their types, random variable example, and others in detail.
Table of Content
- What is Random Variable Meaning
- Variate
- Types of Random Variable
- Discrete Random Variable
- Continuous Random Variable
- Random Variable Formulas
- Random Variable Functions
- Probability Distribution and Random Variable
- Random Variable Example with Solutions
- Practice Problems on Random Variable