The lifetime X (in hundreds of hours) of a certain type of vacuum tube has Weibull distribution with parameters a = 2 and ß = 3.+ Compute the following. (Round your answers to three decimal places.) (a) E(X) and V(X) E(X) = 2.659 V(X) = 1.931 (b) P(X ≤ 5) 0.938 (c) P(2 ≤ x ≤ 5) 0.306 x ✓
The lifetime X (in hundreds of hours) of a certain type of vacuum tube has Weibull distribution with parameters a = 2 and ß = 3.+ Compute the following. (Round your answers to three decimal places.) (a) E(X) and V(X) E(X) = 2.659 V(X) = 1.931 (b) P(X ≤ 5) 0.938 (c) P(2 ≤ x ≤ 5) 0.306 x ✓
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![**The lifetime \(X\) (in hundreds of hours) of a certain type of vacuum tube follows a Weibull distribution with parameters \(\alpha = 2\) and \(\beta = 3\). Compute the following. (Round your answers to three decimal places.)**
**(a) \(E(X)\) and \(V(X)\)**
\[E(X) = 2.659 \quad \text{✔}\]
\[V(X) = 1.931 \quad \text{✔}\]
**(b) \(P(X \leq 5)\)**
\[0.938 \quad \text{✔}\]
**(c) \(P(2 \leq X \leq 5)\)**
\[0.306 \quad \text{✖}\]
**Explanation:**
This exercise involves computing the expected value \(E(X)\), variance \(V(X)\), and probabilities using the Weibull distribution. Calculations are rounded to three decimal places. Part (c) is incorrect.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76fb667-0622-451e-86fc-d3866765f8e5%2F48c8636a-2b88-46c6-b623-09edc3915ea2%2Fpv8a8ul_processed.png&w=3840&q=75)
Transcribed Image Text:**The lifetime \(X\) (in hundreds of hours) of a certain type of vacuum tube follows a Weibull distribution with parameters \(\alpha = 2\) and \(\beta = 3\). Compute the following. (Round your answers to three decimal places.)**
**(a) \(E(X)\) and \(V(X)\)**
\[E(X) = 2.659 \quad \text{✔}\]
\[V(X) = 1.931 \quad \text{✔}\]
**(b) \(P(X \leq 5)\)**
\[0.938 \quad \text{✔}\]
**(c) \(P(2 \leq X \leq 5)\)**
\[0.306 \quad \text{✖}\]
**Explanation:**
This exercise involves computing the expected value \(E(X)\), variance \(V(X)\), and probabilities using the Weibull distribution. Calculations are rounded to three decimal places. Part (c) is incorrect.
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