Let $X$ have a uniform distribution $\operatorname{U}(0,1)$, and let $Y = a + (b-a)X,\, a < b$. (a) Find the distribution function of $Y$. (b) How is $Y$ distributed?
Let $X_1$ , $X_2$ be independent random variables representing lifetimes (in hours) of two key components of a device that fails when and only when both components fail. Say each $X_i$ has an exponential distribution with mean 1000. Let $Y_1 = \min(X_1, X_2)$ and $Y_2 = \max(X_1, X_2)$, so that the space of $Y_1$ and $Y_2$ is $0 < y_1 < y_2 < \infty$. (a) Find $P(Y_1 = y_1, Y_2 = y_2)$ (b) Compute the probability that the device fails after 1200 hours.
distribution questions
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probability
uniform-distribution
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3Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. – 2012-11-08
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1Please note that your post consists of two *unrelated* questions. In general, it is better to put unrelated questions in separate posts. – 2012-11-08