This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Random variables • Discrete random variables. • Continuous random variables. • Discrete random variables . Denote a discrete random variable with X : It is a variable that takes values with some probability. Examples: a. Roll a die. Let X be the number observed. b. Draw 2 cards with replacement. Let X be the number of aces among the 2 cards. c. Roll 2 dice. Let X be the sum of the 2 numbers observed. d. Toss a coin 5 times. Let X be the number of tails among the 5 tosses. e. Randomly select a US household. Let X be the number of people live in this household. • Probability distribution of a discrete random variable X It is the list of all possible values of X with the corresponding probabilities. It can be represented by a table, a graph, or a function. Examples: a. Roll a die. Let X be the number observed. The probability distribution of X is: X P ( X = x ) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6 X P(X=x) 1 2 3 4 5 6 0.00 0.05 0.10 0.15 1 b. Roll two dice. Let X be the sum of the two numbers observed. The probability distribution of X is: X P ( X = x ) 2 1 36 3 2 36 4 3 36 5 4 36 6 5 36 7 6 36 8 5 36 9 4 36 10 3 36 11 2 36 12 1 36 X P(X=x) 2 3 4 5 6 7 8 9 10 11 12 0.00 0.05 0.10 0.15 We can also represent this distribution with a function: P ( X = x ) = 6 x 7  36 , for x = 2 , 3 , ··· , 12. This is called probability mass function and returns the probability for each possible value of the random variable X . • Expected value (or mean) of a discrete random variable It is denoted with E ( X ) or μ and it is computed as follows: Definition: μ = E ( X ) = X x xP ( X = x ) It is a weighted average. The weights are the probabilities....
View
Full
Document
This note was uploaded on 01/14/2011 for the course STATS 100A taught by Professor Wu during the Fall '07 term at UCLA.
 Fall '07
 Wu
 Statistics

Click to edit the document details