POWERPOINT 1 Flashcards
(19 cards)
in algebra, used to represent a numbers whose value is unknown or arbitrary (lower case letter)
variable
a variable whose value is subject to chance, unknown, and unknowable (capital letter)
random variable
a way of characterizing our uncertainty about a random variable; a number between 0 and 1, which describes how likely an event is
probability
P(A)
A is certain to happen, then P(A)=
1
A is certain NOT to happen, then P(A)=
0
the probability of A does not depend on the probability of B
independent events
P(A and B )= P(A) x P(B)
two events cannot occur simultaneously
mutually exclusive events
P(A or B) = P(A) + P(B)
the total probability across all possible events must equal
1
P(not A) =
1-P(A)
describes the behavior of random variables; events are mutually exclusive and probabilities sum to 1
Ex:
X = 0 with prob. .25
1 with prob. .50
2 with prob. .25probability distribution
X is called this when we are able to list all the possible outcomes
discrete random variable
the average value you would get if you repeated the experiment infinitely many times
expected value
k
E(X) =
the expected value of the squared difference between the random variable X and the expectation E(X); it describes how uncertain we are about the expectation
variance
k
Var(X)=
tells us about what can happen to a variable Y for a given value of X; the random variable Y take the value y GIVEN that X equals x
conditional probability
P(Y=y|X=x)
two random variables X and Y are ? if P(Y=y|X=x)=P(Y=y); knowing X tells you nothing about Y
independent
the random variable Y equals y AND the random variable X equals x
joint probability
P(Y=y) and P(X=x) of Y=y and X=x
marginal probability
relationship between the joint, marginal, and conditional
P(X=x|Y=y) = P(X=x, Y=y) / P(Y=y)
relationship between joint and marginal
P(X =x) =
