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Math Help - Discrete Random Variable Question [S1]

  1. #1
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    Discrete Random Variable Question [S1]

    The discrete random variable X has the following probability distribution.
    x = 1, 2. 3 for respective values of
    P(X = x) = θ, 2θ, (1 3θ)
    (a) State the range of possible values of the constant θ. [2]
    (b) Given that E(X) = 22,
    (i) show that θ = 02,
    (ii) calculate the standard deviation of X,
    (iii) evaluate E(1/X) . [10]

    I should be able to do the final parts of this question, but how do I do part a]? I am at a loss for how to approach it despite it looking fairly simple. Could someone please help?
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  2. #2
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    Quote Originally Posted by db5vry View Post
    The discrete random variable X has the following probability distribution.
    x = 1, 2. 3 for respective values of
    P(X = x) = θ, 2θ, (1 – 3θ)
    (a) State the range of possible values of the constant θ.
    P(X = 3) \geq 0

    P(X = 2) \leq 1
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    P(X = 3) \geq 0

    P(X = 2) \leq 1
    For the standard deviation of X, I had 0.75 to 2 decimal places and for E (1/X) I had a value of 17.5.

    Are these values correct?

    Thank you for your help :]
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