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Math Help - Function of random variables

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    Member roshanhero's Avatar
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    Function of random variables

    If X is a random variable with distribution function F(x).Find the distribution of Y=aX+b
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    Hello,

    In general, F denotes the cumulative density function. But please let us know if it is not.

    F(x)=\mathbb{P}(X\leq x)

    So the cumulative density function of aX+b, let's call it G(x) is :
    G(x)=\mathbb{P}(aX+b\leq x)=\mathbb{P}(aX\leq x-b)=\begin{cases} F\left(\tfrac{x-b}{a}\right) \quad \text{if } a>0 \\ 1-F\left(\tfrac{x-b}{a}\right) \quad \text{if } a<0 \\ \text{depends on b if } a=0 \end{cases}
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