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### Chapter 5: Probability Distributions of Discrete Random Variable:

Chapter 5: Probability Distributions of Discrete Random Variable

### Outline:

Outline Random Variables Probability Distribution of a Discrete Random Variable Mean of a Discrete Random Variable Standard Deviation of a Discrete Random Variable Binomial Probability Distribution Poisson Probability Distribution

### Random Variables:

Random Variables A random variable , generally written as X , is a variable whose possible values are numerical outcomes of a random event.

### There are two types of random variables : :

There are two types of random variables : Discrete : can only have whole numbers (no decimal places). Example : Number of cars, houses, fishes, etc. Continuous : can assume any value in one or more intervals. Example : Length, time, weight and price.

### Probability Distribution of a Discrete Random Variable:

Probability Distribution of a Discrete Random Variable A list of probabilities associated with each of its possible values. Characteristics : 0 ≤ P(x) ≤ 1 for each x ∑ P(x) = 1

### Probability Distributions :

Probability Distributions An example will make clear the relationship between random variables and probability distributions. Suppose you flip a coin two times. This simple experiment can have four possible outcomes : HH, HT, TH, and TT. Now, let the variable X represent the number of Heads that result from this experiment. The variable X can take on the values 0, 1, or 2.

### Slide 7:

In this example, X is a random variable ; because its value is determined by the outcome of a statistical experiment. A probability distribution links every outcome of a statistical experiment with its probability of occurrence that is usually shown on a table or in the form of an equation.

### Slide 8:

The following table is an example of a probability distribution of the random variable X. It associates each outcome with its probability. Number of head(s) Probability 0 0.25 1 0.50 2 0.25 