Question

Find the x-value at which f is discontinuous and determine whether f is continuous from the right, from the left, or neither.

1) Continuous from the right
2) Continuous from the left
3) Discontinuous at x = 0
4) Discontinuous at x = 6

Answer 1

The student's question focuses on calculating probabilities within continuous probability distributions, emphasizing that the probability of exact values in such distributions is always zero and probabilities are determined over intervals.

Step-by-step explanation:

The question asked relates to continuous probability functions and specific scenarios involving these functions, such as calculating the probability P(x) in given conditions for continuous probability distributions. This is explored through a series of sub-questions.

Which involve understanding properties of continuous functions and applying these to calculate probabilities. It's important to note that for a continuous probability distribution, the probability of a single, exact value, like P(x = c), is always 0 because the values are uncountably infinite in any range. Instead, probabilities are calculated over an interval.

For a probability distribution where a function f(x) is defined, questions typically ask for probabilities associated with certain ranges or conditions, like P(x > 15), P(x = 7), or P(x < 0). In these cases, the concepts of area under the probability density function and properties of uniform distributions usually come into play.

For instance, since probabilities in a continuous distribution are determined by the area under the curve between two points on the x-axis, the probability that x is exactly one of those points is zero.