Random Variables And Its Probability Distributions
Chapter Name : Probability |
Sub Topic Code : 104_12_13_06_03 |
Topic Name : Random Variables And Its Probability Distributions |
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Sub Topic Name : Mean Of A Random Variable |
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Introduction
• The most important characteristics of any probability distribution is the mean or average value. • The mean of a random variable is the sum of products of all possible values by their respective probabilities.
Pre-Requisites:
• Knowledge of probability. • Knowledge of Random variables, mean.
Activity:
X is a measure of location or central tendency.
Real Life Question:
An insurance company sells car insurance policy of $8000 for a premium of $300 per year. The probability of car damage in the year following purchase of policy is 0.1%. What is the expected gain for this policy?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Probability | Probability is the chance that something will happen. |
| Mean value | Middle or average value. |
| Random Variables | A random variable is a numerical value that represents outcomes of an experiment. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Two coins. | Toss two coins and the random variable X is the number of heads when the coin is tossed. Find the mean of X. |
Real life uses :
Mean of a random variable can be used in many real life scenarios as finding mean profit of a business, calculating number of orders, calculating number of defective pieces in production run etc.
Places to visit :
Find the height of family members and find the mean value.
Practical examples around us
| Examples | Explainations |
|---|---|
| Mean of random variable in business. | Chemical company sells its customers chemicals in 5 pound bags. Let x = number of lots ordered by randomly selected customer and x has the following probability 0.4, 02, 0.3, 0.1. Now mean number of lots ordered by a customer can be calculated by mean of random variable. |
What you learn in Theory:
Mean of a random variable is the sum of products of all possible values of random variable with its respective probabilities.
What you learn in Practice:
Mean of a random variable is the middle or average value. Mean of random variable is used for calculating profit associated with a policy of insurance company.