lecture 16

Question 1

how probability is used to compute P(A) - theorem of tot prob

Answer 1

P(A ∩ Bk) = P(A|Bk) = 0
for some k

Question 2

describe bayes theorem

Answer 2

for 2 events A and B with P(A) >0 and P(B) >0
P(B|A)= P(A|B) P(B)/P(A)

Question 3

describe bayes theorem - expansion

Answer 3

if 0<P(B)<1
THEN
P(B|A)= P(A|B) P(B)/P(A|B) P(B) + P(A|B^C) P(B^C)
USING theorem tot prob

Question 4

can bayes theorem apply to many numbers

Answer 4

yeeee - sum of them under, like using total prob theorem

Question 5

when can we add conditional probs - bayes theorem

Answer 5

only when conditioning on same event

Question 6

when is bayes theorem often used

Answer 6

to make probability statements concerning an event B that has NOT BEEN observed given event A that HAS BEEN observed

Question 7

what is the Prosecutor’s Fallacy:

Answer 7

P(spots|measles) does NOT EQUAL P(measels|spots)
P(evidence|guilt) DOES NOT equal P(guilt|evidence)

Question 8

bayes theorem can extend to

Answer 8

Multiple events
2 conditional events
chain rule applied to bayes theorem