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Math Help - Small DRV question [S1]

  1. #1
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    Small DRV question [S1]

    The probability distribution of the discrete random variable X is given in the following:
    For x = 1, 2, 3, 4, 5.
    P(X=x) = 0.3, p, 0.1, q, 0.05.


    (a) Show that p + q = 0·55. [1]
    (b) Given that E(X) = 2·75, show that p = 0·15 and q = 0·4. [4]
    (c) Find the variance of X. [3]
    (d) The random variable Y is defined by Y = 4X + 2.
    (i) Find the mean and variance of Y.
    (ii) Find P(Y < 15). [6]

    I have got all the way to the second part of (d).
    for c, I calculated the variance of X to be 1.8875.
    for d1] the mean was 14 and the variance was 30.2.

    How is P(Y < 15) found?
    It's probably something very simple. Thank you if you can steer me in the right direction as to what it is
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  2. #2
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    Quote Originally Posted by db5vry View Post
    The probability distribution of the discrete random variable X is given in the following:
    For x = 1, 2, 3, 4, 5.
    P(X=x) = 0.3, p, 0.1, q, 0.05.


    (a) Show that p + q = 0·55. [1]
    (b) Given that E(X) = 2·75, show that p = 0·15 and q = 0·4. [4]
    (c) Find the variance of X. [3]
    (d) The random variable Y is defined by Y = 4X + 2.
    (i) Find the mean and variance of Y.
    (ii) Find P(Y < 15). [6]

    I have got all the way to the second part of (d).
    for c, I calculated the variance of X to be 1.8875.
    for d1] the mean was 14 and the variance was 30.2.

    How is P(Y < 15) found?
    It's probably something very simple. Thank you if you can steer me in the right direction as to what it is
    I haven't checked your calculations - I assume you know what you're doing and can do basic arithmetic.

    As to the specific question you've asked ..... What values of X will make Y < 15? What's the probability of getting those values of X?
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