Financial Risk Manager Part 1
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A discrete random variable Y has probability function given by:
| Y | 0 | 1 | 2 |
|---|---|---|---|
| P(Y = y) | 0.3 | 0.6 | 0.1 |
Calculate Var(Y).
Other
Community
NNikitesh
A
0.2
B
0.36
C
0.8
D
1
Explanation:
The variance of a discrete random variable is calculated using the formula: Var(Y) = E(Y²) - [E(Y)]²
Step 1: Calculate E(Y) E(Y) = Σ [y × P(Y=y)] = (0 × 0.3) + (1 × 0.6) + (2 × 0.1) = 0 + 0.6 + 0.2 = 0.8
Step 2: Calculate E(Y²) E(Y²) = Σ [y² × P(Y=y)] = (0² × 0.3) + (1² × 0.6) + (2² × 0.1) = (0 × 0.3) + (1 × 0.6) + (4 × 0.1) = 0 + 0.6 + 0.4 = 1
Step 3: Calculate Var(Y) Var(Y) = E(Y²) - [E(Y)]² = 1 - (0.8)² = 1 - 0.64 = 0.36
Therefore, the correct answer is B) 0.36.
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