3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous ran- dom variable with cumulative distribution function F(x) = {{ 1 - 8x x < 0, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.
3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous ran- dom variable with cumulative distribution function F(x) = {{ 1 - 8x x < 0, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.
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![**Problem 3.14:**
The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with the cumulative distribution function:
\[
F(x) =
\begin{cases}
0, & x < 0, \\
1 - e^{-8x}, & x \geq 0.
\end{cases}
\]
Find the probability of waiting less than 12 minutes between successive speeders:
(a) Using the cumulative distribution function of \(X\).
(b) Using the probability density function of \(X\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b3f294e-d3c8-4475-8e8e-f2b525027412%2F2400a924-96ca-4ab0-a561-f2f37b042741%2Fhpu5kjf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3.14:**
The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with the cumulative distribution function:
\[
F(x) =
\begin{cases}
0, & x < 0, \\
1 - e^{-8x}, & x \geq 0.
\end{cases}
\]
Find the probability of waiting less than 12 minutes between successive speeders:
(a) Using the cumulative distribution function of \(X\).
(b) Using the probability density function of \(X\).
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