Chapter 5
2 variables are said to be __________________ if Pሺሼܺൌݔሽ&ሼܻൌݕሽሻ ൌ ܲሺܺ ൌ ݔሻ ∙ ܲሺܻ ൌ ݕሻ for all x and y.
independent
The Bernoulli Trials are ____.
independent
In other words, if the _________ probability equals the _______________ of the ___________________ probabilities.
joint; product; marginal
Probability ____________________: A ______________ of the possible _________ and corresponding ______________ of a discrete random variable, or a formula for the probabilities.
Distribution: listing;values; probabilities
F is for
Failure
Sum of the probabilities of a discrete random variable
For any discrete random variable X we have the summation of E P(X=x)=1
Probability ___________________: A __________ of the probability distribution that displays the ____________________________ of a discrete random variable on the horizontal axis and the probabilities of those values on the vertical axis
Histogram: graph; possible values
S is for
Success
Example: A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls. a) Identify the possible values of the random variable X. b) Determine the probability distribution of X.
a) 0,1,2,3,4
When two balanced dice are rolled, 36 equally likely outcomes are possible. Let Y denote the sum of the dice. a) What are the possible values of the random variable Y? b) Use random variable notation to represent the event that the sum of the dice is 7. c) Find P(Y=7)
a) 2,3,4,5,6,7,8,9,10,11,12 b){y=7} c) 1/6
Example: In the game of craps, a first roll of a sum of 7 or 11 wins, whereas a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is rolled. Determine the probability of the following: a) A win on the first roll. b) A loss on the first roll.
a) P(win)=P(y=7)+P(y=11)=6/35+2/36=8/36-2/9 b)P(lose)=P(y=2)+P(y=3)+P(y=12)=1/36+2/36+1/36=4/36=1/9
The _________________ distribution is the probability distribution for the number of _______________ in a sequence of ________________ trials.
binomial; successes; Bemoulli
A ________________ random variable is a random variable whose possible values can be listed.
discrete
Suppose we wish to represent the event that a student has two siblings. We represent an ___________ with braces.____________ read as "X equals 2". We express the __________________ of the event as ____________ read as "the probability that X = 2".
event; {x=2} ;probability; P{x=2}
Bernoulli Trails: The success ________________ denoted ___ remains the same from trial to trail.
probability; p
A ____________________ is a quantitative variable whose value depends on chance.
random variable
The _________________________ of a discrete random variable is denoted x or, simply if no confusion will arise.
standard deviation
The __________________ of a discrete random variable is the standard deviation squared, ____.
variance
