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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.4 Probability and Calculus, #3 · Probability · Continuous distributions

### *4 If …, show that the probability … that … is…

Why is $p (x) = e^{- 2 x}$ not an acceptable probability density for $x \geq 0$ ? Why is $p (x) = 4 e^{- 2 x} - e^{- x}$ not acceptable?

### *4
If $p_{n} = (\frac{1}{2})^{n}$ , show that the probability $P$ that $X$ is a prime number satisfies $6/16 \leq P \leq 7/16$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.4 Probability and Calculus, #3

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