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

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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: \( \frac{11}{42} \)
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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