# Consider $X \sim \text{Unif} (\alpha, \beta)$. Find $P(X<\alpha + p(\beta - \alpha))$ Assume $p$ is a constant with $0<p<1$

Consider $X \sim \text{Unif} (\alpha, \beta)$. Find $P(X<\alpha + p(\beta - \alpha))$ Assume $p$ is a constant with $0<p<1$

-
hey new user. Your questions will be much more elegant and easy to answer if you use latex to typeset. Also, mention the source and outline your attempts for a solution. Tag homework if relevant. Cheers! –  dexter04 Dec 12 '12 at 1:28

$X \sim Unif(\alpha, \beta)$
Find $\mathbb{P}(X<\alpha +\rho (\beta - \alpha))$ with $0<p<1$
Supposing that we have a continuous uniform distribution, we have the cumulative distribution function is $\mathbb{P}(X \le x) = \frac{x-\alpha}{\beta-\alpha}$ if $\alpha \leq x \le \beta$. This is just $\frac{\alpha +\rho (\beta - \alpha) - \alpha}{\beta - \alpha} = \rho$. Specifically, $\mathbb{P}(..) = 0$ for $\rho = 0$.