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Stats CH 5 section 3 and 4
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Terms in this set (20)
conditional probabilites
where we focus on just one group of objects and imagine taking a random sample from the group alone
often conditional probabilities are worded with the phrase
given that
venn diagram
representing all of the data
green overlap region represents in venn diagram
the event of something AND something
conditional equation
P(A|B)=P(A and B)/ P(B) doesn't matter which event is called A and which event is called B
a common mistakes with conditional probabilities is thinking
P(A|B) is the same as P(B|A), P(B|A)= 1/P(A|B), it is impossible for a probability to be bigger than 1
associated
because the conditional probabilities change depending on which educational level we condition on
independent events
we call variables or events that are not associated, P(A|B)= P(A)
sometimes you can use what to decide whether two events are independent
intuition
common challenge in probability is to find probabilities for
sequences of events
when dealing with sequences it is helpful to
determine where the events are independent or associated, if associated then conditional probabilities is useful so use P(A and B)= P(A)P(B|A)
multiplication rules
if the events are independent then we use P(B|A)= P(B)
when two events are independent that multiplication rule speeds up probability calculations for events joined by
AND
do not use the multiplication rule if events are
not independent
if events are not independent then we rely on probability rule 5b
P(A and B)= P(A) P(B|A)
law of larger numbers
theorem that tells us that if our simulation is designed correctly then the more trials we do the closer we can expect our empirical probability t come to the true probability, reason why simulations are useful
with small number of trials our empirical probability was
far away than when it was done with more trials
when you dont get the right value two explanations are possible
theoretical value is incorrect, your empirical probability is just varying thats why empirical probabilities do, you can make it very less and get closer to the theoretical value by doing
how many trials should you do before using a computer simulation
100
if you flip a coin many times who should happen to the proportion of the heads as the flips increase
.5
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