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Getting the cumulative distribution function for this continuous random variable. Watch

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    I need to find the median for this random variable, X, and whilst I can sketch it easily and find it, I'd like to know how to do it using the cumulative distribution function.

    The Probability density function of X:

    1/4 if 0≤x≤1

    3/4 if 1<x≤2

    0 otherwise.

    Apparently the median = 4/3.

    Thanks in advance!
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    To find the CDF, you'll need to integrate the first part of the PDF to find F[x] and add that onto the integral of the second part. Reply to me and I'll post a picture if you need to
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    (Original post by zomgleh)
    I need to find the median for this random variable, X, and whilst I can sketch it easily and find it, I'd like to know how to do it using the cumulative distribution function.

    The Probability density function of X:

    1/4 if 0≤x≤1

    3/4 if 1<x≤2

    0 otherwise.

    Apparently the median = 4/3.

    Thanks in advance!
    Using CDF you should to solve an inequality system for m
    \displaystyle \int_{-\infty}^m dF(x) \ge \frac{1}{2}
    \displaystyle \int_{m}^{\infty} dF(x) \ge \frac{1}{2}

    The integrals are Riemann-Stieltjes integrals
    More simple to calculate median from PDF
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    (Original post by 24DJF)
    To find the CDF, you'll need to integrate the first part of the PDF to find F[x] and add that onto the integral of the second part. Reply to me and I'll post a picture if you need to
    Ok so I got the Cumulative distribution function to be--
    0 for x<0

    x/4 for 0≤x≤1

    3x/4 - 1/2 for 1<x≤2

    1 for x>2


    But how do I know which one to choose in order to get the median?
    F(m)=0.5 ?
    Apparently it's the '3x/4 - 1/2 for 1<x≤2' one.
 
 
 
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