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Math Help - Discrete probability

  1. #1
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    Discrete probability

    Firstly, I'm sorry if I'm posting an advanced question in the basic section, but I'm pretty sure this belongs here.

    I took stats a few years ago and my course right now doesn't have a textbook so I'm not sure exactly how this is done.

    Question reads: "The random variable X takes on one of the values 1,2,3,4,5 with probabilities
    P(X=i) = ki, i = 1,2,3,4,5
    for some value k. Find P(2 <= X <= 3)."

    I'm not looking for a straight answer, just a question of where to start. I'm not sure but I thought that the sum of all P(X) across the domain of X (here [1,5]) should equal 1. So technically I should be able to solve for k right?

    P(X) = kx
    P(1) + P(2) + P(3) + P(4) + P(5) = 1.0
    k + 2k + 3k + 4k + 5k = 1.0
    14k = 1.0
    k = 1/14
    therefore:
    P(X) = x/14

    In which case the probability that X is 2 or 3 should be:

    P(2 <= X <= 3) = P(2) + P(3) = 2/14 + 3/14 = 5/14

    Is that right? or am I doing something entirely different?
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  2. #2
    Moo
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    Hello,

    Perfect reasoning

    except that 1+2+3+4+5=15, not 14
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  3. #3
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    Oops... You are of course correct Moo. I'm really surprised my logic isn't in some way flawed (even if my implementation is).


    Thanks a lot!
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  4. #4
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    Quote Originally Posted by sadmath View Post
    Question reads: "The random variable X takes on one of the values 1,2,3,4,5 with probabilities
    P(X=i) = ki, i = 1,2,3,4,5
    for some value k. Find P(2 <= X <= 3)."

    I'm not looking for a straight answer, just a question of where to start. I'm not sure but I thought that the sum of all P(X) across the domain of X (here [1,5]) should equal 1. So technically I should be able to solve for k right?

    P(X) = kx
    P(1) + P(2) + P(3) + P(4) + P(5) = 1.0
    k + 2k + 3k + 4k + 5k = 1.0
    14k = 1.0
    k = 1/14
    therefore:
    P(X) = x/14

    In which case the probability that X is 2 or 3 should be:

    P(2 <= X <= 3) = P(2) + P(3) = 2/14 + 3/14 = 5/14
    You have a small error. k=\frac{1}{\color{blue}15}
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  5. #5
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    Thanks for the reply Plato, but I think Moo beat you to the punch
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  6. #6
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    Quote Originally Posted by sadmath View Post
    Thanks for the reply Plato, but I think Moo beat you to the punch
    She beats most people to the punch (she's that kind of cow).
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  7. #7
    Moo
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    Quote Originally Posted by mr fantastic View Post
    She beats most people to the punch (she's that kind of cow).
    I prefer beating people to (drinking) ponch
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