Notes

1a) Definition when A & B are mutually exclusive
b) Definition when A&B are independent
c) give examples for both definitions above
d) Sets, given a sample space of (1,2,3...) for A &B and determine whether or not they're independent. i.e if P(A)intersectP(B)=P(A)*P(B)
e)Prove P(C) is independent from P(A Union B)
f)Are mutually exclusive events independent?
g)Prove P(A union B)=P(A)*P(B') + P(B)
h) Give an example of an infinitely countable and uncountably infinite set
i)State the definition of conditional probablility
j)Using Q table find the values...
2) There is a shipment of beads and criminals are trying to smuggle in diamonds along with the beads. There is 1 diamond in every 1000 beads. But as it passes the border, only 100 beads are inspected, determine the probability that the criminals get caught. (I think you use Poisson Thm. here)
3) Similar to the 1st question in the practice midterm. There is a test conducted and 0.01 people who take the test have a diesease, the population at risk is 0.3, and the chance of getting a false positive is 0.1 determine the probability of actually having the disease. (Using baye's theorem)
4a)Given a function fx(c(x+x^2) from 0<x<3 and 0 otherwise determine the constant c
b)determine the CDF of the function above
c) Determine the probability of P(1<x<3/2), (x=4/3)
d) What is the expectation of the CDF
e)Determine the PDF of the function