You are given the following discrete uniform probability distribution of gross profits from purchase of an option:
| Profit | Cumulative Distribution Function |
| $0 | 0.2 |
| $1 | 0.4 |
| $2 | 0.6 |
| $3 | 0.8 |
| $4 | 1.0 |
The probability of a profit greater than or equal to $1 and less than or equal to $4 is closest to:
C is correct. There are two ways to find P(1 ≤ X ≤ 4):
1) Find the sum of four probabilities: P(1), P(2), P(3), and P(4), 0.2 + 0.2 + 0.2 + 0.2 = 0.8.
OR
2) Calculate the probability as the difference between the two values of the cumulative distribution function.
In this case, F (4) = P(X ≤ 4) = 1.0 and F(1) = P(X ≤ 1) = 0.2.
Therefore, P (1 ≤ X ≤ 4) = 1.0 – 0.2 = 0.8.