Bayes’ theorem describes the probability of an event, based on conditions that
Might be related to the event. Bayes’ theorem can also be calculated as the
Joint probability divided by the marginal.
Bayes’ theorem deals with conditional probability.
????(????) ∗ ????(????|????) = ????(????) ∗ ????(????|????)
????(????|????)=P(Ai)P(B|Ai)/ P(A1)P(B|A1)+ P(A2)P(B|A2)
????(????|????)=P(Ai ∩B) / P(A1∩B)+P(A2∩B)
-Discrete probab distrib(numb of students absent today, numb of books borrowed from library, number of head appering when a cons is tossed tre time)LIMITED
-Conitnous:liter of rain that occur in barcelona, the wheight of all population in spain )UNLIMITED.
Not because If not P(X)=P(X|favor of law) and They aren’t
Saco numero de hab(tot rev/prof) y despues (sumatoria profit Por room dividido numero de room)
BINOMIAL probability distribution
A widely Occurring discrete probability distribution Only two possible outcomes for each trial of an experiment (success & failure) .Outcomes mutually exclusive Probability of success remains the same from one trial to another .Each trial Is independent from any other trial.Examples:
-Probability of answering correctly a question In a multiple- choice test. Outcome: correct/incorrect
-Probability of producing a defective product. Outcome: defective/acceptable
The binomial probability is computed by the Formula:
????(????)= n????x ????x(1−????)n-x
n: number of trials
x: number of successes
π: probability of a success on each trial
. Suppose you are given two choices: either you are paid 12,000 now or you are paid 15,000 at the end of a ten-month period. You also know that the projection for the inflation rate is 2 percent per month then answer.
A) which one of the two would you choose and why?
= 1.02 a la 10 =1.219, implying and increase of 22 percent in prices. Delating now yields 15,000/1.219 =12,305 which is more than 12,000. Also, 12,000 today are equal to 12,000 * 1.219=14,628 dollars at the end of ten month period. In both cases we get better numbers for second alternative. Notice that the ratio between both possible answers is the same, or 12,000/12,305 and 14,628/15,000 which is 0,97 we should choose the second option that is to be paid 15,000 later
B. What should be the monthly inflation rate that would make you indifferent between the two alternatives? You can assume as before, that the inflation rate be the same for all months
X a la 10=15,000/12,000 then x= raiz 10 de (1.25) and x=1.0225, and the inflation that makes you indifferent to the alternatives is 2.25 percent monthly.
-Wich group Is more homegnous? The One with lower CV.
-What Conclusion I can ge? Group (a/b) has higher spending and investment than the Other, and that the dispersion of investmen in group(a/b) is higher that in the Other that is more concertated.
-Determine whether x And y are independent and why. fij=f(x)f(y) is not fulfilled