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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### Probability Density Function of a Discrete Random Variable The probability density function of a discrete random variable \( X \) is provided in the following table: \[ \begin{aligned} P_X(X = 1) &= 0.05 \\ P_X(X = 2) &= 0.10 \\ P_X(X = 3) &= 0.12 \\ P_X(X = 4) &= 0.30 \\ P_X(X = 5) &= 0.30 \\ P_X(X = 6) &= 0.11 \\ P_X(X = 7) &= 0.01 \\ P_X(X = 8) &= 0.01 \\ \end{aligned} \] ### Tasks 1. **Compute \(E(X)\)**. 2. **Compute \(Var(X)\)**. 3. **Compute \(P(X \leq 5)\)**. 4. **Compute \(P(X > 3)\)**.
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Transcribed Image Text:### Probability Density Function of a Discrete Random Variable The probability density function of a discrete random variable \( X \) is provided in the following table: \[ \begin{aligned} P_X(X = 1) &= 0.05 \\ P_X(X = 2) &= 0.10 \\ P_X(X = 3) &= 0.12 \\ P_X(X = 4) &= 0.30 \\ P_X(X = 5) &= 0.30 \\ P_X(X = 6) &= 0.11 \\ P_X(X = 7) &= 0.01 \\ P_X(X = 8) &= 0.01 \\ \end{aligned} \] ### Tasks 1. **Compute \(E(X)\)**. 2. **Compute \(Var(X)\)**. 3. **Compute \(P(X \leq 5)\)**. 4. **Compute \(P(X > 3)\)**.
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