Question

For a continuous distribution, is it true that p(x ≤ 100) = p(x < 100)?

Answer 1

For a continuous distribution, P(X ≤ x) and P(X < x) are equivalent and have the same value.

Step-by-step explanation:

For a continuous distribution, P(X ≤ x) is the probability that the random variable X is less than or equal to x. On the other hand, P(X < x) is the probability that the random variable X is strictly less than x. Since the continuous distribution has an uncountable infinite number of outcomes, the probability of a specific point value is zero. Therefore, P(X ≤ x) and P(X < x) are equivalent and have the same value.