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Math Help - Detemine A (random variable)

  1. #1
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    Detemine A (random variable)

    A random variable X has pdf
    <br />
f(x)=\begin{cases}<br />
Ax \; , \qquad \qquad 0 \le x < 5\\ <br />
A(10 - x) \;  , \qquad 5 \le x < 10 \\<br />
0 \; , \qquad otherwise<br />
\end{cases}


    i) Determine A
    ii) Find P(2.5 \le X \le 7.5)
    Last edited by mr fantastic; May 4th 2009 at 04:18 PM.
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  2. #2
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    Quote Originally Posted by Stats View Post
    A random variable X has pdf
    <br />
f(x)=\begin{cases}<br />
Ax \; , \qquad \qquad 0 \le x < 5\\ <br />
A(10 - x) \; , \qquad 5 \le x < 10 \\<br />
0 \; , \qquad otherwise<br />
\end{cases}


    i) Determine A
    ii) Find P(2.5 \le X \le 7.5)
    As with most of the questions you have asked, apply the basic definitions and formulas:

    i) Use the fact that \int_{- \infty}^{+ \infty} f(x) \, dx = 1.
    ii) Calculate \int_{2.5}^{7.5} f(x) \, dx = 1.

    Note that the rule for f(x) is different over different intervals.
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