Expected number of profitable trades

Question

A desk places 4 trades today. Based on the models, they each turn a profit with probabilities 0.55, 0.60, 0.45, and 0.70 respectively. On average, how many of the 4 trades are profitable?

Accepted Answer

Put one indicator on each trade: Xi = 1 if trade i is profitable. Then E[Xi] is that trade's profit probability. The number of profitable trades is X = X1 + X2 + X3 + X4, and by linearity of expectation E[X] = 0.55 + 0.60 + 0.45 + 0.70 = 2.3. Takeaway. Expected successes equal the sum of individual success probabilities, here 0.55 + 0.60 + 0.45 + 0.70 = 2.3 profitable trades on average.

Expected number of profitable trades

Your answer

More Probability questions