Final answer:
The student is studying the probability distribution function of a continuous random variable and how to determine its cumulative distribution function (CDF).
Step-by-step explanation:
The student's question pertains to a Continuous random variable's probability distribution function, particularly in understanding its cumulative distribution function (CDF). The given function, f(x) = ⅓(1 − x) for 0 ≤ x ≤ 1, describes the probability density of a continuous random variable X within the specified range. To find the CDF, one needs to integrate f(x) from the lower bound (here, 0) up to a certain value x.
The CDF, denoted as P(X ≤ x), shows the probability that X takes on a value less than or equal to x. To calculate P(X > x), which is the area to the right of x, you use the identity P(X > x) = 1 − P(X ≤ x). It's important to remember that for continuous distributions, the probability at a single point is zero, which means P(x = c) = 0 for any value of c.