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November 2003 S1 Question

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    How would you do part a)? The mark scheme has me stumped :/
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    (Original post by Dirtyflanker)
    How would you do part a)? The mark scheme has me stumped :/
    Its a discrete uniform distribution, so use the formula,  E(X) = \dfrac{n+1}2
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    (Original post by raheem94)
    Its a discrete uniform distribution, so use the formula,  E(X) = \dfrac{n+1}2
    I did that but to get all the marks you have to derive it from the probability distribution
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    (Original post by Dirtyflanker)
    I did that but to get all the marks you have to derive it from the probability distribution
     \displaystyle E(X) = \sum x \times P(X=x) = \frac1n + \frac2n + \frac3n + \cdots + \frac{n}{n} = \frac{1}{n} ( 1 + 2 +3+ \cdots + n)

    Use  \displaystyle \frac{n}2(2a+(n-1)d) for  ( 1 + 2 +3+ \cdots + n)

     \displaystyle  \frac{1}{n} ( 1 + 2 +3+ \cdots + n) = \frac{1}{n} \left( \frac{n}2 \left(2 + (n-1)1 \right) \right) = \frac1n \left( \frac{n}2 (n+1) \right) = \frac{n+1}2

    Now input the values and find  n
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    Wow, thanks wouldn't have expected the need for that formula in an s1 exam though :s
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    help me please..... who knows how to do the probabiltity question q2..
    q: a fairground game involves trying to hit a moving target with a gunshot. a round consists of up to 3 shots. ten points are scored if a player hits the target, but the round is over if the player misses. linda has a constant probability of 0.6 of hitting the target and shots are INDEPENDENT OF ONE ANOTHER. (WHAT DOES THIS MEAN, HOW CAN I SHOW IT ON A TREE DIAGRAM OR ISIT A VENN DIAGRAM??)

    a) find the probability that linda scores 30 points in a round

    The r.v X is the no. of points linda scores in a round.
    b) find the probability distribution of X
    c) find the mean n SD of X

    A game consists of 2 rounds
    d)find the probability that linda scores more points in round 2 than in round 1.
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    Don't have the answers in front of me, but I sort of remember doing it a while back:
    a) P(HHH) = 0.6 x 0.6 x 0.6
    b) x 0 10 20 30
    P(x)0.4 0.6x0.4 0.6x0.6x0.4 0.6x0.6x0.6

    See the tree diagram attached. By independent- it just means that the probability of the next event happening is not dependent on the previous probability ie- a hit is always 0.6 and a miss is always 0.4.

    c) Just use the formulas
    d) Always write out what the possibilities are, so if she needs more points in round 2 than in round 1 you can write it out as:

    Round 2 Round 1
    P(10) P(0) Multiply each set together and add up all the probabilities and that's your answer Click image for larger version. 

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    P(20) P(0)
    P(30) P(0)
    P(20) P(10)
    P(30) P(10)
    P(30) P(20)

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Updated: May 17, 2012
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