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The probability density function for the number of times a child screams during…

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Wize University Calculus 2 Textbook > Applications of Integrals

Probability

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The probability density function for the number of times a child screams during a roller coaster is given by
f(x)={16π(1−cos⁡(2x)),0≤x≤6π0,otherwisef(x) = \left \{ \begin{array}{ll} \displaystyle \frac{1}{6 \pi}(1 - \cos(2x)), & 0\leq x \leq 6 \pi \\\\ 0, & \text{otherwise} \end{array} \right .
Find the mean number of screams over the course of the ride.




More Probability Questions:
Let XX be a random variable with values that range within [0,2][0, 2] with pdf
p(x)=38x2p(x) = \frac{3}{8}x^2
Compute the mean, and standard deviation of this distribution.
Let XX be a continuous random variable with a probability density function
f(x)={ce−4x,0≤x0,otherwisef(x) = \left \{ \begin{array}{ll} ce^{-4x}, & 0 \leq x \\ 0, & \text{otherwise} \end{array} \right .
First, determine the value of cc that makes the function a PDF. Then determine P(9≤X≤11)P(9 \leq X \leq 11) .