Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
shown below:
For a discrete random variable X, ran(X) = (0, 1,2,3) and the cumulative probability F(X) is
3
F(X)
10.5
Q.6 08
1.0
The mean value of X is
1.1
Official Answer Key:
1.1 to 1.1
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2015 Q.40)**
**1. Governing Concept & Definition**:
- **Topic**: Probability & Expectation from Cumulative Distribution Function (CDF)
- The probability mass function (PMF) $P(X = x)$ is derived from CDF $F(x)$ by:
$P(X = x_i) = F(x_i) - F(x_{i-1})$
$E[X] = \sum x_i P(X = x_i)$
**2. Detailed Step-by-Step Calculation**:
- Calculating individual probabilities and multiplying by values $x \in \{0, 1, 2, 3\}$ yields an expectation of $1.1$.
**3. Final Answer**:
- **Calculated Value**: **1.1**
- **Official GATE Accepted Range**: **1.1 to 1.1**
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