The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0. f(x) = if æ < 12 if x > 12 Find the following: P(X > 23) = -0.895 The cumulative distribution function of X: if æ < 12 F(x) = 1-(12/x) if æ > 12 The probability that at least one out of 7 devices of this type will function for at least 40 months: 11/42
The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0. f(x) = if æ < 12 if x > 12 Find the following: P(X > 23) = -0.895 The cumulative distribution function of X: if æ < 12 F(x) = 1-(12/x) if æ > 12 The probability that at least one out of 7 devices of this type will function for at least 40 months: 11/42
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![The probability density function of \( X \), the lifetime of a certain type of device (measured in months), is given by
\[
f(x) =
\begin{cases}
0 & \text{if } x \leq 12 \\
\frac{12}{x^2} & \text{if } x > 12
\end{cases}
\]
Find the following: \( P(X > 23) = -0.895 \)
The cumulative distribution function of \( X \):
\[
F(x) =
\begin{cases}
0 & \text{if } x \leq 12 \\
1 - (12/x) & \text{if } x > 12
\end{cases}
\]
The probability that at least one out of 7 devices of this type will function for at least 40 months: \( \frac{11}{42} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e0d396c-e5f5-46c2-813a-9ed0820c37ca%2F1be9bfd9-9774-4d6e-8afe-30cdbd880157%2Fd4764i_processed.png&w=3840&q=75)
Transcribed Image Text:The probability density function of \( X \), the lifetime of a certain type of device (measured in months), is given by
\[
f(x) =
\begin{cases}
0 & \text{if } x \leq 12 \\
\frac{12}{x^2} & \text{if } x > 12
\end{cases}
\]
Find the following: \( P(X > 23) = -0.895 \)
The cumulative distribution function of \( X \):
\[
F(x) =
\begin{cases}
0 & \text{if } x \leq 12 \\
1 - (12/x) & \text{if } x > 12
\end{cases}
\]
The probability that at least one out of 7 devices of this type will function for at least 40 months: \( \frac{11}{42} \)
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