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Math Help - probability of error in interval

  1. #1
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    probability of error in interval

    in certain experiments the error made in determining the solubility of a substance is a RV having uniform density with alpha=-0.025 and beta=0.025 What are the possibilities that such an error is between
    1)0.010 and 0.015
    2)-0.012 and 0.012

    i am thinking of applying uniform distribution as random variable of uniform density is given.But how to use the constants alpha and beta in it

    please help
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  2. #2
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    Re: probability of error in interval

    The probability density function of a uniform random variable is f(x)=\frac{1}{\beta- \alpha}
    If you integrate that over a range you will find the probability of being in that range.
    Thanks from prasum
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  3. #3
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    Re: probability of error in interval

    Quote Originally Posted by prasum View Post
    in certain experiments the error made in determining the solubility of a substance is a RV having uniform density with alpha=-0.025 and beta=0.025 What are the possibilities that such an error is between
    1)0.010 and 0.015
    2)-0.012 and 0.012

    i am thinking of applying uniform distribution as random variable of uniform density is given.But how to use the constants alpha and beta in it

    please help
    $p_E(e)=\begin{cases}\dfrac 1 {\beta-\alpha}&e \in [\alpha, \beta]\\\\ 0 &\mbox{else}\end{cases}$

    $Pr[E < e]=\begin{cases}0 &e<\alpha \\ \\ \dfrac{e-\alpha}{\beta-\alpha}&\alpha \leq e \leq \beta \\\\1 &\beta < e\end{cases}$
    Thanks from prasum
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