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Assume that the amount of evidence against a defendant in a criminal trial is an exponential random variable X. If the defendant is innocent, then X has mean 1, and if the defendant is guilty, then X has mean 2. The defendant will be ruled guilty if X>c, where c is a suitably chosen constant. If the judge wants to be 95% certain that an innocent man will not be convicted, what should the value of c be? Enter your answer as a decimal and make sure that at least 8 digits after the decimal point are correct.

I'm a little confused on how to approach this. I think the constant C is really messing me up. Help please

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You want to find $c$ such that $P(X < c) = 0.95$, where $X$ is an exponential random variable with mean $1$ (as it is if the defendant is an innocent man: it doesn't say what the judge would do if the defendant were a woman).

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