{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson 5 Random Variable and Probability Distribution

# Lesson 5 Random Variable and Probability Distribution -...

This preview shows pages 1–5. Sign up to view the full content.

Random Variables and Probability Distributions Definitions: Random Variable – is a function that associates a real number with each element in the sample space. Discrete Random Variable – a random variable which takes on a finite or countable number of values. Nondiscrete or Continuous Random Variable – is a random variable that takes on a non-countable or infinite number of values.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Examples: 1. Classify the following random variables as discrete or continuous: a. The number of traffic accidents occurring at a certain intersection b. The volume of gasoline sold from a certain gasoline station c. Proportion of people who patronize a certain brand of clothing d. Shelf life of bread sold in the grocery e. Number of eggs laid each month by a hen f. Number of applicants in a certain University 2. Let W be a certain random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W.
Discrete Probability Distribution The set of ordered pairs (x , f(x) ) is a probability function, probability mass function, or probability distribution of the discrete random variable X if , for each possible outcome x, 1. 2. 3. Note: 1. The cumulative distribution function F(x) of a discrete random variable X with probability distribution f(x) is 2. The graph of f(x) is a probability histogram. f ( x ) 0 f ( x ) = 1 x F ( x ) = P ( X x ) = f ( t ) , for - < t x x < P ( X = x ) = f ( x )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example An experiment consists of tossing 3 fair coins. Let X denotes the number number of tails which come up. With each sample point we can associate a number for X, a random variable. Find the probability function and the distribution function of X. Draw the probability histogram.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}