Final answer:
The question pertains to finding the probability for a given range in a continuous probability distribution, where the function does not satisfy typical probability density function properties. Instead, insights from uniform distribution are provided, showing how probabilities are determined by the area under the curve within a given interval.
Step-by-step explanation:
The student is asking about a continuous probability distribution where the function f(x) is defined as f(x) = 1.5x2 for -1 < x < 1, and f(x) = 0 otherwise. To determine the probability P(0 < X), we would integrate the function from 0 to 1 (since the function is 0 after x = 1).
However, the function provided in the example does not seem to be a proper probability density function since it does not integrate to 1 over its range. For a probability density function, the area under the curve between the specified range must equate to the probability.
As per the concept of uniform distribution mentioned in the question, if we consider a function f(x) = 1/10 for 0 ≤ x ≤ 10, then P(0 < x < 4) would be the area under the curve from 0 to 4, which is (4 − 0)(1/10) = 0.4, indicating a probability of 0.4. For a uniform distribution, the area under the curve for any interval is simply the base of the interval times the uniform height of the distribution.