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प्रश्न
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?
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उत्तर
Let X be the random variable of getting profit in a business
| X | 2000 | – 1000 |
| P(X = x) | 0.4 | 0.6 |
E(x) = Σxxpx(x)
= (0.4 × 2000) + [0.6 × (– 1000)]
= 800 – 600
E(X) = 200
∴ Expected value of profit = ₹ 200
E(X2) = Σx2 Px(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
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