Financial Risk Manager Part 1

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Explanation:

We are given that X = 2Y + 10
This implies that:
V[X] = V[2Y + 10] = 4V[Y]

But we know that,
V[Y] = E[Y²] - (E[Y])²
= 0.3 * 0² + 0.2 * 1² + 0.4 * 2² + 0.1 * 3² - [0.3 * 0 + 0.2 * 1 + 0.4 * 2 + 0.1 * 3]²
= 2.7 - 1.7 = 1

Hence, V[X] = 4V[Y] = 4 * 1 = 4

Logic applied:
I. V[aX] = a²V[X]
II. V[X ± a] = V[X]

Where X is a random variable, and a is a constant.

Q.67 Let Y be a discrete random variable with the following probability distribution:

Y 0 1 2 3
P(Y = y) 0.3 0.2 0.4 0.1

Determine the variance of X, where X = 2Y + 10

Y	0	1	2	3
P(Y = y)	0.3	0.2	0.4	0.1

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RRohit

Last updated: June 22, 2026 at 14:25

1.7.

2.7.