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Consider the following function. f(x) = x1/7, a = 1, n = 3, 0.9 ≤ x ≤ 1.1

User Scofield
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Final answer:

In continuous probability functions, probabilities are determined by areas under the curve within a specified range. A single value in such a distribution has zero probability, and the entire range under the function sums to a probability of

Step-by-step explanation:

Exploring Continuous Probability Functions

When analyzing continuous probability functions, there are several key elements to consider. The function f(x) defined on a certain interval represents a probability density, where the total area under the graph between the given interval equates to a probability of 1. If the function is given as f(x) = x1/7 within the interval 0.9 ≤ x ≤ 1.1, we can explore specific probabilities within this range.

However, if we are considering a horizontal line such as f(x) = 20 for 0 ≤ x ≤ 20, the probability is distributed equally among all values of x. Therefore, the probability of a particular value of x, say P(x = 7), is zero since for a continuous distribution, a single point does not have an area and thus has no probability assigned to it.

For a function restricted between 0 and a certain value, such as 0 ≤ x ≤ 7, the probability of x being greater than this range, e.g. P(x > 10), would be zero as well, since the function does not exist beyond x = 7 in this scenario. Evaluating a probability for an interval within the function's range, such as P(0 < x < 12) for a function defined up to x = 12, would yield a probability of 1, as it represents the entire range of the distribution.

User Saeed All Gharaee
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