Statistics Help: Please Read?

Posted by: robbie1975c  /  Category: Uncategorized

Question by GQSLC: Statistics Help: Please Read?
Catalog Sales: You are the marketing director for a museum that raises money by selling gift items from a mail-order catalog. For each catalog sent to a potential customer, the customer’s entry in the data file is Y if they ordered something and N if they did not ( Y= yes, N= no). After you have mailed the fall and winter catalogs, you estimate the probabilities of buying patterns based on those who recieved the catalogs as follows:

Outcome (fall, winter): YY YN NY NN
Probablitity: 0.30 0.10 0.05 0.55 (respectively)

a) Let F denote buying from the fall catalog and W denote buying from the winter catalog. Find P(F) and P(W)

b) Explain what the event “F and W” means, and find
P(F and W)

c) Are F and W independent events? Explain why you would not normally expect customer choices to be independent.

Thanks!!

Best answer:

Answer by northridgeville
fall,winter
Y,Y =.30
Y,N =.10
N,Y =.05
N,N =.55
———-
=1.00
===============================
p(F)=Y,Y,N,N= 0.50
p(W)=Y,N,Y,N= 0.50
———–
b) Explain what the event “F and W” means, and find P(F and W)
Means a sale from both catalogs.
p(f)*p(w)=.5*.5=.25
——————————
c) Are F and W independent events? Explain why you would not normally expect customer choices to be independent.

Not independent events, someone who buys in the fall is more likey to buy from winter catalog–know they seller, know process, statified, liited sources for the buyer, etc….
Not expected to be independent because history shows p(F&W)=.30 not expect .25 if they were independent events.

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One Response to “Statistics Help: Please Read?”

  1. Arturo B Says:
    August 8th, 2010 at 3:48 pm

    a) According to the law of Total Probability, P(F)=∑P(F and Bn), so using all the probabilities that include a Y, P(F)=P(Y and Y) + P(Y and N) + P(N and Y) = 0,45
    P(W)=P(Y and N) + P(N and Y) + P(N and N) = 0,70. It is not possible that P(W) and P(F) are the same because P(Y and Y) is much smaller then P(N and N)

    b) It means that both have to happen, and the answer is P(W and F) = 0,45 * 0,70 = 0,315

    c) They are independent events, because there is no information about conditional probability, like the probability of buying from the winter catalog if you bought from the fall catalog P(W|F)., so this probability is equal to P(W)

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