Question

In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?

Answer 1

Let X be the random variable of getting profit in a business

X	2000	– 1000
P(X = x)	0.4	0.6

E(x) = Σ_xxp_x(x)

= (0.4 × 2000) + [0.6 × (– 1000)]

= 800 – 600

E(X) = 200

∴ Expected value of profit = ₹ 200

E(X²) = Σx² P_x(x)

= [(2000)² × 0.4] + [(– 1000)² × 0.6]

= (4000000 × 0.4) + (1000000 × 0.6)

E(X²) = 2200000

Var(X) = E(X²) – [E(X)]²

= 22000000 – (200)²

= 2200000 – 40000

Var(X) = 21,60,000

Variance of his profit = ₹ 21,60,000

Standard deviation(S.D) = `sqrt("Var"(x))`

σ = `sqrt(2160000)`

σ = 1469.69

Standard deviation of his profit is ₹ 1,469.69