# Thread: probability of error in interval

1. ## 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

2. ## 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.

3. ## Re: probability of error in interval

Originally Posted by prasum
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

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