Exam (elaborations)
UGA BIOSTAT EXAM 2
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Exam of 19 pages for the course UGA BIOSTAT at UGA BIOSTAT (UGA BIOSTAT EXAM 2)
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UGA BIOSTAT EXAM 2the mathematical foundation upon which biostatistics is built - - Probability
- To understand why we can trust random samples and randomized
comparative experiments, we must look at _____________ - - chance behavior
- __________________ is unpredictable in the short run but has a regular and
predictable pattern in the long run - - chance behavior
- a phenomenon is called __________ if individual outcomes are uncertain but
there is a regular distribution of outcomes in a large number of repetitions -
- random
- ____________ is the chance that an uncertain event will occur - - probability
- __________________ refers to the _______________ of times an event is
expected to occur a very long series of identical repetitions - - probability,
proportion
- When considering probability, we deal with random phenomena that
produces outcomes, such - - •rolling a die
•answering a multiple-choice test question
•undergoing a pregnancy test
- any outcome or set of outcomes of a random phenomenon - - an event
- Events are denoted by - - capital letters
•Examples:
A = The event that a coin toss results in Heads
B = The event that a randomly chosen student is male
- The ______________________ of a random phenomenon is the set of all
possible outcomes - - sample space S
- When an event has been defined in a way that allows for counting, we can
determine its probability by - - counting the number of ways it can occur and
dividing by the total number of possible events
- The probability that event A will happen - - P(A)
- Any probability is a number between - - 0-1
- an event with a probability of 0 - - never occurs
,- an event with a probability of 1 - - always occurs
- all possible outcomes together must have a probability of - - 1
- If S is the sample space of a random phenomenon, then P(S) = - - 1
- Since an outcome must occur on every trial, the sum of the probabilities
for all possible outcomes must be exactly - - 1
- it is often beneficial to represent probability problems graphically using - -
Venn diagrams
The entire sample space is usually represented by a rectangular box, and
individual events are represented by shapes inside the box.
•All possible outcomes are contained in the box
•The area inside the box represents the total probability of the sample
space.
•The total area inside the box must
be 1.
•The area inside shapes within the box represent the probabilities of
individual events.
•The area inside shapes within the
box must be between 0 and
- The probability than an event does not occur is _____________________ - - 1 -
the probability that the event does occur
- If an event occurs 70% of the time, - - it fails to occur 30% of the time
- the event that A does not happen - - A bar, called "A complement"
- For any event A - - P(A bar) = 1 - P(A)
- The _______ of events two events A and B is the _____ that either A or B (or
both) occurs - - union, event
- the union of events A and B is denoted - - A U B
Thus, the probability that either of the events, A or B, occurs is P(A or B) =
P(A U B)
- Two events A and B are ______ or ______________ is they ____________ occur
at the same time (dying by falling off a building and getting shot - only one
kills you) - - disjoint, mutually exclusive, cannot
- If, and only if, A and B are disjoint - - P(A U B) = P(A) + P(B)
-this is the addition rule for disjoint events
, - The probability that either A happens or B happens is simply - - the sum of
the 2 probabilities
- The _____________ of two events A and B is the _______ that both A and B
occur - - intersection, event
The intersection of events A and B is denoted A∩B.
•Thus, the probability that both events, A and B, occur is P(A and B)= A ∩ B
- In probability, we generally associate the word _____ with multiplication - -
and
- P(A and B) = - - P(B and A)
- Two events are said to be ___________ if the occurrence of one event does
not affect the likelihood of the other event - - independent
- Two events A and B are ________________ if knowing that one occurs does
not change the probability that the other occurs - - independent
- If, and only if, two events, A and B, are independent, then - - P(A∩B) =
P(A)P(B)
- You rolled a die and flipped a coin. What is the probability of getting a 3 on
the face of the die and getting a head on the coin - - A = the number on the
die is 3 (P(A) = 1/6)
B = The coin turns up heads (P(B) = 1/2)
P(A cap B) = (1/6)(1/2) = 1/12
- The probability of rolling any number on the die in no way influences the
probability of getting a head (or a tail) on the coin, so - - A and B are
independent
- You __________ just assume that two events are independent! - - cannot
- You cant assume that two events are independent. Sometimes you can
apply logic and reasoning, like with tossing coins and rolling a die, but
_________ - - rarely
- If you do not know that two events are independent you _____ assume that
they are _____ independent and you ______ use this formula:
P( A cap B) = P(A)P(B) - - Must, not, cannot
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