Random variables and probability distributions
This document discusses random variables and probability distributions. It defines a random variable as a quantitative outcome of a random experiment that can take on different values. Random variables are represented by capital letters. It provides examples of random variables like the number on a die or number of tails in coin tosses. Random variables can be discrete, taking a finite number of values, or continuous, taking infinitely many values. A probability distribution shows the probabilities of all possible outcomes of a discrete random variable, with probabilities between 0 and 1 that sum to 1. The mean and standard deviation of a discrete random variable are also defined. The mean is the expected value, while the variance measures the spread from the mean and the standard deviation is the square root of the
![Mean and Standard Deviation of a
Discrete Random Variables
Variance of a random variable is defined as the
measure of spread for a distribution that
determines the degree to which the values of a
random variable differ from the expected value.
Thus,
Var (X) = E(X)2 – [E(X)]2
(Note: (variance)2 = standard deviation](https://image.slidesharecdn.com/randomvariablesandprobabilitydistributions-201011090859/85/Random-variables-and-probability-distributions-8-320.jpg)
Random variables and probability distributions
- 1. Chapter 2 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
- 2. Random Variables A set of possible values from a random experiment. It is a quantitative variable whose value is the result of an event or experiment. It is represented by an upper case letter, such as X, Y, or Z. It is called random because it can take different values. Lower case letters are used to represent the actual values from the experiment.
- 3. Random Variables Example: Experiment Random Variable 1. Rolling a die X = number facing up when rolling a fair die 2. Tossing a coin ten times X = number of tails in ten tosses 3. Randomly picking a student and measuring his/her weight X = weight of the student
- 4. Types of Random Variables 1. Discrete Random Variable - if it only takes a finite number of distinct values. - It has a countable number of possible values.
- 5. Types of Random Variables 2. Continuous Random Variable - if it only takes infinitely many possible values. - it can take values that are measured on a continuous scale.
- 6. Probability Distribution Only applicable to all discrete random variable. It shows the probabilities associated with all possible outcomes. It must satisfy the following conditions: - each probability must be between 0 and 1. - the sum of all the probabilities is 1.
- 7. Mean and Standard Deviation of a Discrete Random Variables Expected Value (EV) is equal to the mean of the random variable. It is the average of the values assumed by the random variable in repeated trials of the experiment. Thus, (EV) μ = E(X) = X1P1 + X2P2 + X3P3….. XnPn
- 8. Mean and Standard Deviation of a Discrete Random Variables Variance of a random variable is defined as the measure of spread for a distribution that determines the degree to which the values of a random variable differ from the expected value. Thus, Var (X) = E(X)2 – [E(X)]2 (Note: (variance)2 = standard deviation