A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Help me answer questions B & C

**(b)** Calculate \( P(X \leq 4) \). [Input box for answer] How does this probability compare to \( P(X < 4) \)? - \( P(X \leq 4) > P(X < 4) \) - \( P(X \leq 4) < P(X < 4) \) - \( P(X \leq 4) = P(X < 4) \) **(c)** Calculate \( P(3.5 \leq X \leq 4.5) \). [Input box for answer] Calculate \( P(4.5 < X) \). [Input box for answer]
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Transcribed Image Text:**(b)** Calculate \( P(X \leq 4) \). [Input box for answer] How does this probability compare to \( P(X < 4) \)? - \( P(X \leq 4) > P(X < 4) \) - \( P(X \leq 4) < P(X < 4) \) - \( P(X \leq 4) = P(X < 4) \) **(c)** Calculate \( P(3.5 \leq X \leq 4.5) \). [Input box for answer] Calculate \( P(4.5 < X) \). [Input box for answer]
The current in a certain circuit as measured by an ammeter is a continuous random variable \( X \) with the following density function: \[ f(x) = \begin{cases} 0.05x + 0.3 & \text{for } 3 \leq x \leq 5 \\ 0 & \text{otherwise} \end{cases} \] This function describes the probability density of measuring a particular current, \( x \), within the specified range. For values of \( x \) less than 3 or greater than 5, the probability density is zero, meaning such measurements are not possible under this model.
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Transcribed Image Text:The current in a certain circuit as measured by an ammeter is a continuous random variable \( X \) with the following density function: \[ f(x) = \begin{cases} 0.05x + 0.3 & \text{for } 3 \leq x \leq 5 \\ 0 & \text{otherwise} \end{cases} \] This function describes the probability density of measuring a particular current, \( x \), within the specified range. For values of \( x \) less than 3 or greater than 5, the probability density is zero, meaning such measurements are not possible under this model.
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