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Math Help - Please help, continuous random variable problem..

  1. #1
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    Please help, continuous random variable problem..

    1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).

    2)suppose X1...Xn are independent identically distributed random variables, each with distribution function Fx(x). Let M be the largest of the {Xi}. express the event 'M<=x' as an intersection of n independent events, each involving exactly one of the {Xi}. hence deduce that the distribution function of M is Fm(x)=[Fx(x)]^n

    3)use results of 1) and 2) to write down expression for the distribution function of the largest among n independent U(0,θ) random variables. find the corresponding density function.
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  2. #2
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    Quote Originally Posted by kevek View Post
    1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).

    [snip]
    Read this thread: http://www.mathhelpforum.com/math-he...-question.html

    I might have time for the others later.
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  3. #3
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    Quote Originally Posted by kevek View Post
    1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).

    2)suppose X1...Xn are independent identically distributed random variables, each with distribution function Fx(x). Let M be the largest of the {Xi}. express the event 'M<=x' as an intersection of n independent events, each involving exactly one of the {Xi}. hence deduce that the distribution function of M is Fm(x)=[Fx(x)]^n

    3)use results of 1) and 2) to write down expression for the distribution function of the largest among n independent U(0,θ) random variables. find the corresponding density function.
    The ideas you need for 2) are in this thread: http://www.mathhelpforum.com/math-he...ease-help.html

    If you're still stuck, please show where.

    Where are you stuck in 3)?
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    The ideas you need for 2) are in this thread: http://www.mathhelpforum.com/math-he...ease-help.html

    If you're still stuck, please show where.

    Where are you stuck in 3)?
    Thank you very much.
    In part 3) i don't understand what is 'U( )' and what is corresponding density function
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  5. #5
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    Quote Originally Posted by kevek View Post
    Thank you very much.
    In part 3) i don't understand what is 'U( )' and what is corresponding density function

    For 2) this thread might also help: http://www.mathhelpforum.com/math-he...-question.html

    U(0,θ) means the uniform distribution on the range (0,θ).
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