Final answer:
The value of the cumulative distribution function f(x) at x=1.5 is 0.125. This is calculated by substituting x with 1.5 into the given function and simplifying.
Step-by-step explanation:
The student's question pertains to finding the value of the cumulative distribution function (cdf) for a given random variable x at a specific point. According to the function provided, f(x) = (x-1)²/2 for the range 1 < x < 2. Therefore, to find f(1.5), we substitute x with 1.5.
If we calculate it, f(1.5) = ((1.5-1)²)/2 = (0.5²)/2 = 0.25/2 = 0.125. Consequently, the value of f(1.5) is 0.125, which corresponds to option 2 in the question posed by the student.
This type of problem is commonly found in courses dealing with probability and statistics, and understanding the properties of continuous random variables is crucial. Unlike discrete random variables that have distinct outcomes, continuous ones have outcomes that can take on a full range of values, hence why the probability is calculated over an interval