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Math Help - Probability Homework - Is it correct?? HELP!

  1. #1
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    Probability Homework - Is it correct?? HELP!

    How can I do the second one?

    Can someone be extremely helpful ?
    Question 3 (Unit 1)
    – 10 marks
    (a)
    The random variables V
    and W
    have the following probability generating
    functions.
    (i)
    ΠV (s)= 7s / 10 - 3s

    (ii)
    ΠW (s)= (7 + 3s / 10 ) power of 8

    Use the table of discrete probability distributions on page 4 of the Handbook
    to identify the distribution of each of the random variables. In each case, you
    should name a family of distributions and give the values of any parameters.
    p(X=x)

    I haven't got a clue how to do it

    (b)
    The number of items bought by each customer entering a chemist’s shop is a
    random variable Xthat has a geometric distribution starting at 0 with mean
    1.5.

    (i)
    Find the value of the parameter pof the geometric distribution and
    hence write down the probability generating function of X.

    (ii)
    Six customers visit the shop. The number of items bought by a
    customer is independent of the number bought by any other customer.
    Write down the probability generating function of Y, the total number
    of items they buy. Use the table of discrete probability distributions on
    page 4 of the Handbook to identify the distribution of Y, and hence find
    the mean and variance of the total number of items purchased by the six
    customers.
    Last edited by mr fantastic; March 8th 2009 at 03:05 PM. Reason: Deleted duplicate questions posted in other threads.
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  2. #2
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    Is it correct??

    i) Mean(x) = P/Q = 1.5
    where q = 1- p so using the P.G.F for a Geometric Distribution we have

    P/1-P = 1.5
    2.5.P = 1.5
    Result P= 0.6 and Q=0.4

    Probability Generating Function would be = q/ 1-ps

    p.g.f(x)= 0.4 / 1 - 0.6s

    Is it correct?? Do I need to do anything else?

    thanks
    Last edited by mr fantastic; March 8th 2009 at 03:00 PM. Reason: No edit, just flagging this post as being moved from a duplicate thread
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  3. #3
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    Quote Originally Posted by wallace View Post
    [snip]
    Question 3 (Unit 1)
    – 10 marks
    (a)
    The random variables V
    and W
    have the following probability generating
    functions.
    (i)
    ΠV (s)= 7s / 10 - 3s

    (ii)
    ΠW (s)=  (7 + 3s / 10 ) power of 8

    Use the table of discrete probability distributions on page 4 of the Handbook
    to identify the distribution of each of the random variables. In each case, you
    should name a family of distributions and give the values of any parameters.
    p(X=x)

    I haven't got a clue how to do it

    Mr F says: Have you looked at page 4? Which ones have the same form as what you've been given ....?

    (b)
    The number of items bought by each customer entering a chemist’s shop is a
    random variable Xthat has a geometric distribution starting at 0 with mean
    1.5.

    (i)
    Find the value of the parameter pof the geometric distribution and
    hence write down the probability generating function of X.

    Mr F says: It should be obvious that you would solve (1 - p)/p = 1.5 .... Now substitute p into the relevant pgf.

    (ii)
    Six customers visit the shop. The number of items bought by a
    customer is independent of the number bought by any other customer.
    Write down the probability generating function of Y, the total number
    of items they buy. Use the table of discrete probability distributions on
    page 4 of the Handbook to identify the distribution of Y, and hence find
    the mean and variance of the total number of items purchased by the six
    customers.
    You should go back and have another think. Post your progress after you've done this.
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  4. #4
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    Quote Originally Posted by wallace View Post
    How can I do the second one?

    Can someone be extremely helpful ?
    Question 3 (Unit 1)
    – 10 marks
    (a)
    The random variables V
    and W
    have the following probability generating
    functions.
    (i)
    ΠV (s)= 7s / 10 - 3s

    (ii)
    ΠW (s)= (7 + 3s / 10 ) power of 8

    Use the table of discrete probability distributions on page 4 of the Handbook
    to identify the distribution of each of the random variables. In each case, you
    should name a family of distributions and give the values of any parameters.
    p(X=x)

    I haven't got a clue how to do it

    (b)
    The number of items bought by each customer entering a chemist’s shop is a
    random variable Xthat has a geometric distribution starting at 0 with mean
    1.5.

    (i)
    Find the value of the parameter pof the geometric distribution and
    hence write down the probability generating function of X.

    (ii)
    Six customers visit the shop. The number of items bought by a
    customer is independent of the number bought by any other customer.
    Write down the probability generating function of Y, the total number
    of items they buy. Use the table of discrete probability distributions on
    page 4 of the Handbook to identify the distribution of Y, and hence find
    the mean and variance of the total number of items purchased by the six
    customers.
    These questions form part of a graded assessment. Thread closed.
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