quiz 5 Flashcards
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the probability of event A given that event B has occurred is called the…
CONDITIONAL probability of A, given that B has occurred
how is the vertical bar read as
given
the conditional probability of event A given that B has occurred is…
P(A∩B)/P(B)
when 2 events are independent, the conditional probability equals the marginal probability of the event
P(A|B)=P(A)
a _________ is the event that the test is positive for a given condition, given that the person _____ have the condition
false positive(type I error), does not
a_________ is the event that the the test is negative for a given condition, given that the person______ the condition
false negative (type II error), has
a sample space can be partitioned into k subplots that are…
mutually exclusive and exhaustive
the law of total probability
P(A)= P(S1) x P(A|S1) + P(S2) x P(A|S2) +…..
P(A∩Si)=
P(Si) x P(A|Si)
a variable X is a ________ if the value that it assumes corresponding to the outcome of an experiment , is a chance or random event
random variable
quantitative variables are either________ or________, according to the values that x can assume
discrete, continuous
we defined probability as the limiting value of the _____________ as the experiment is repeated over and over again
relative frequency
Now we define the probability distribution for a random variable as the_________ constructed for the entire population of measurements
relative frequency distribution
the _________ for a discrete random variable is a formula, table, or graph that gives all the possible values of x, and the probability( p(x)=P(X=x) ) associated with each value x
probability distribution
the difference is that the relative frequency distribution describes a_______ of n measurements while the probability distribution is constructed as a model for the entire ________ of measurements
sample, population
The population mean which measures the average value of x in a population is also called the __________ of the random variable X and is written as ______. It is the value that you would expect to observe _______
expected value, E(x), on average
E(x)= ∑ x p(x)
true
σ²=∑ (x-ϻ)² p(x)
true
a binomial experiment is one that has ____ characteristics
5
1.the experiment consists of n ____ trials
identical
- Each trial results in one of ___ outcomes, one outcome is called a success and the other a failure
2
- The probability of success on a single trial is equal to _____ and remains the same from trial to trial. the probability of failure is ____=q
p, 1-p
- The trials are ________
independent
- We are interested in the ______ random variable X, the # of successes in n trials, for X=0,1, n
discrete
mean for binomial random variable
ϻ= np
variance for binomial random variable
σ²=npq
the values of x are mutually exclusive, summing p(.) over all values of x is the same as adding the probabilities of all simple events and therefore equals.
true
requirement 1 for discrete probability distribution
p(x) is greater than or equal to 0 and less than or equal to 1
requirement 2 for discrete probability distribution
∑ p(x)=1
what is the general multiplication rule ?
The probability that both A and B occur when the experiment is performed is
P(A∩B)= P(A) P(B|A)
2 mutually exclusive events are not independent of each other
true or false
TRUE
2 events are independent if….
the conditional probability of that event is equal to the marginal probability of that event and if P(A∩B)= P(A)P(B)
