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Probability density function of a random variable X is given below f(x) = { 0.25 if 1 ≤ x ≤ 5 { 0 otherwise P(X ≤ 4) is

1. 3/4
2. 1/2
3. 1/4
4. 1/8

Correct answer: 3/4

Solution

The probability P(X ≤ 4) is calculated by integrating the probability density function from 1 to 4, which gives the area under the curve. Since the function is constant at 0.25 over the interval from 1 to 5, the area from 1 to 4 is 0.25 times the length of the interval (3), resulting in 0.75 or 3/4.

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