statistical experiment
is a process that, when performed results in one and only one of many observations
sample point
an element of a sample space
event
includes one or more outcomes
simple event
includes one and only one outcome
compound event
at least two outcomes
The experiment of tossing a coin 4 times has
16 outcomes
2 x 2 x 2 x 2 = 16 or 24 = 16
A box contains a few red, a few black, and a few white marbles. Two marbles are randomly drawn from this box and the color of these marbles is observed. The total number of outcomes for this experiment is:
9
32 = 9
RRRBRW BBBRBW WWWRWB
You randomly select two households and observe whether or not they own a telephone answering machine.
Exactly one of them owns a telephone answering machine is a simple event.
You toss a coin nine times and observe 3 heads and 6 tails. This event is a
simple event
The probability of an event is always
between 0 and 1, inclusive
According to the relative frequency concept of probability, the probability of an event is
the number of times the given event is observed divided by the total number of repetitions of the experiment
conditional probability
is a probability
that an event will occur given that another event has already occurred
marginal (simple) probability
probability of an event without considering any other event
Two mutually exclusive events____?
cannot occur together
Two events are independent if the occurrence of one event
does not affect the probability of the occurrence of the other event
Two events are independent if the occurrence of one event
does not affect the probability of the occurrence of the other event
Two complementary events
taken together include all outcomes for an experiment
Two events A and B are independent if
P(A|B) is equal to P(A)
If PA B P(A)P(B), then events A and B are
independent
random variable
a variable whose value is determined by the outcome of a random experiment
discrete random variable
a random variable: whose set of values is countable
continuous random variable
a random variable that can assume any value in one or more intervals
probability distribution table of a discrete random variable
all of the values that the random variable can assume and their corresponding probabilities
mean of a discrete random variable
the mean of its probability distribution
mean of a discrete random variable
is its expected value
The formula used to obtain the mean of a discrete random variable is
zxP(x)
The standard deviation of a discrete random variable is
the standard deviation of its probability distribution
n! "n factorial" represents
the product of all integers from n to 1
The factorial of zero
is 1
The number of combinations for selecting zero elements from 8 distinct elements is
is 1
The number of combinations for selecting 14 elements from 14 distinct elements is
is 1
A court randomly selects a jury of 7 persons from a group of 16 persons. The total number of combinations is
11440
Condition of a binomial experiment:
1) There are n identical trials
2) Each trial has two and only two outcomes
3) p is the probability of success, q is the probability of failure, and p + q = 1
4) The trials are independent
binomial experiments, the outcome called a "success" is
an outcome to which the question refers
parameters of the binomial probability distribution are
n and p
binomial probability distribution is symmetric if
p is equal to .50
binomial probability distribution is right-skewed if
p is less than .50
The binomial probability distribution is left-skewed if
p is greater than .50
The mean of a binomial distribution is equal to:
np
The standard deviation of a binomial distribution is equal to
square root of npq
Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 13 such college graduates hired recently by companies, exactly 5 wil
P(5) = 0.0022
The joint probability of two independent events A and B is the Multiplication Rule for Independent Events
P(A and B) = P(A)P(B)
The joint probability of two mutually exclusive events is always equal to
0.00
The probability that a person is a college graduate is 0.34 and that he/she has high blood pressure is 0.15. Assuming that these two events are independent, the probability that a person selected at random is a college graduate and has high blood pressure
P(G and H) = 0.34 x 0.15 = 0.051
The union of two events A and B represents the outcomes that are
either in A or in B or in both A and B