The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .073 Px(X = 1) = .117 Px(X = 2) = .258 Px(X = 3) = .322 %3D Px(X = 4) .230 i) Compute E(X). ii) Compute Var(X).
The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .073 Px(X = 1) = .117 Px(X = 2) = .258 Px(X = 3) = .322 %3D Px(X = 4) .230 i) Compute E(X). ii) Compute Var(X).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 10E
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![**Probability Density Function and Statistical Calculation**
The probability density function of a discrete random variable \(X\) is given by the following table:
\[P_X(X = 0) = 0.073\]
\[P_X(X = 1) = 0.117\]
\[P_X(X = 2) = 0.258\]
\[P_X(X = 3) = 0.322\]
\[P_X(X = 4) = 0.230\]
To solve the given problems:
i) **Compute \(E(X)\):**
The expected value \(E(X)\) of a discrete random variable \(X\) can be calculated using the formula:
\[E(X) = \sum_{i} x_i \cdot P(X = x_i)\]
ii) **Compute \(Var(X)\):**
The variance \(Var(X)\) is given by:
\[Var(X) = E(X^2) - [E(X)]^2\]
Where \(E(X^2)\) is the expected value of the square of \(X\) and can be calculated as:
\[E(X^2) = \sum_{i} x_i^2 \cdot P(X = x_i)\]
These calculations involve summing over all the possible values of \(X\) weighted by their respective probabilities. Substituting the given values from the table will provide the numerical results for \(E(X)\) and \(Var(X)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45fdd75f-924d-4ac4-9d15-03fc1f26bc02%2Fa20673dc-387b-409a-9d50-b00135fa6d68%2Fzns79r_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability Density Function and Statistical Calculation**
The probability density function of a discrete random variable \(X\) is given by the following table:
\[P_X(X = 0) = 0.073\]
\[P_X(X = 1) = 0.117\]
\[P_X(X = 2) = 0.258\]
\[P_X(X = 3) = 0.322\]
\[P_X(X = 4) = 0.230\]
To solve the given problems:
i) **Compute \(E(X)\):**
The expected value \(E(X)\) of a discrete random variable \(X\) can be calculated using the formula:
\[E(X) = \sum_{i} x_i \cdot P(X = x_i)\]
ii) **Compute \(Var(X)\):**
The variance \(Var(X)\) is given by:
\[Var(X) = E(X^2) - [E(X)]^2\]
Where \(E(X^2)\) is the expected value of the square of \(X\) and can be calculated as:
\[E(X^2) = \sum_{i} x_i^2 \cdot P(X = x_i)\]
These calculations involve summing over all the possible values of \(X\) weighted by their respective probabilities. Substituting the given values from the table will provide the numerical results for \(E(X)\) and \(Var(X)\).
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