Final answer:
The probability that a continuous random variable X in a uniform distribution over the interval (a-1, a+1) takes on the value of a is zero, because in a continuous distribution, the probability of taking on any single specific value is always zero.
Step-by-step explanation:
The student is asking about the probability that a continuous random variable X, defined on the interval (a-1, a+1), takes on the specific value of a. In the context of uniform distribution, a continuous random variable has equally likely outcomes over a specified domain. However, for a continuous distribution, the probability of the variable taking any single specific value is always zero because there are an infinite number of possible values it can take within any interval. Therefore, even though the outcomes are equally likely in a uniform distribution, the probability that X takes the specific value of a is 0.
This concept is often tricky for those new to statistics because it differs from how we consider probabilities for discrete variables, where there's a finite set of possible outcomes. The uniform distribution is represented by the notation X~U(a, b), and its probability density function (pdf) is shaped like a rectangle, indicating all outcomes in the interval are equally likely.