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Math Help - Error in probability question?

  1. #1
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    Error in probability question?

    Hi guys,

    I believe there are one or two errors in the wording of this problem and I need to make sure I know what they are before I actually do this problem. The problem reads:

    Suppose that R is a random variable f_R(x) =\frac{3}{8}x^2 for x \in [0, 2] Let Y = X^3
    (a) Find F_Y(y)

    (b) Find f_y(y)

    Would it make more sense for the problem to read "Suppose that X (instead of R)is a random variable..." and f_X(x) = \frac{3}{8}x^2 instead of f_R(x) = \frac{3}{8}x^2?

    Also, for (a) and (b), did the author mean "Find F_Y(x)" and "Find f_Y(x)" instead of F_Y(y) and f_Y(y) respectively?

    Thanks for any help!

    James
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    Re: Error in probability question?

    Quote Originally Posted by james121515 View Post
    Hi guys,

    I believe there are one or two errors in the wording of this problem and I need to make sure I know what they are before I actually do this problem. The problem reads:

    Suppose that R is a random variable f_R(x) =\frac{3}{8}x^2 for x \in [0, 2] Let Y = X^3
    (a) Find F_Y(y)

    (b) Find f_y(y)

    Would it make more sense for the problem to read "Suppose that X (instead of R)is a random variable..." and f_X(x) = \frac{3}{8}x^2 instead of f_R(x) = \frac{3}{8}x^2?

    Also, for (a) and (b), did the author mean "Find F_Y(x)" and "Find f_Y(x)" instead of F_Y(y) and f_Y(y) respectively?

    Thanks for any help!

    James
    R is a random variable that depends on x. There's nothing wrong with that, it's just unusual notation.

    (a) and (b) are correctly stated in the question.
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    Re: Error in probability question?

    To clarify, f_R(x) is the probability density function for the random variable R (or X, and big X and big Y are random variables as well. Not sure if that changes anything?
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    Re: Error in probability question?

    Quote Originally Posted by james121515 View Post
    To clarify, f_R(x) is the probability density function for the random variable R (or X, and big X and big Y are random variables as well. Not sure if that changes anything?
    I have given my opinion on the wording of the question as posted in post #1. I do not understand your so-called clarification. Are you saying the question is NOT as worded in post #1?
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    Re: Error in probability question?

    Thanks for your replies.

    The question is worded exactly as in the original post, except for a small typo on my part it should have been:

    (b) f_Y(y) and not f_y(y)

    If the wording of the problem is correct, could you please help me understand the question. Since our pdf f_R(x) is for the random variable R, woudn't we need some relationship between R and X, and then from X to Y (which we have since Y=X^3) in order to do this?

    Best,
    James
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    Re: Error in probability question?

    Quote Originally Posted by james121515 View Post
    Thanks for your replies.

    The question is worded exactly as in the original post, except for a small typo on my part it should have been:

    (b) f_Y(y) and not f_y(y)

    If the wording of the problem is correct, could you please help me understand the question. Since our pdf f_R(x) is for the random variable R, woudn't we need some relationship between R and X, and then from X to Y (which we have since Y=X^3) in order to do this?

    Best,
    James
    OK, looking at it closer I see what you mean. It would make sense to be asked to find the pdf for Y = R^3 since the question does not define the random variable X anywhere.

    I suggest you ask whoever set the question. I recant my earlier opinion and would suggest there is a typo in the definition of Y.
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