Asked by Jennifer Bennett on Sep 27, 2024
Verified
Which of the following is true about f(x) when X has a uniform distribution over the interval [a,b]?
A) The values of f(x) are different for various values of the random variable X.
B) f(x) equals one for each possible value of X.
C) F(x) equals one divided by the length of the interval from a to b.
D) None of these choices.
Uniform Distribution
A type of probability distribution where all outcomes are equally likely over a certain range of values.
Probability Density
A function that describes the relative likelihood for a random variable to take on a given value, primarily used in continuous probability distributions.
Random Variable
A variable that takes on a range of values determined by a random phenomenon, and it's described by its probability distribution.
- Understand the concept of the uniform distribution and its probability density function (PDF).
Verified Answer
YD
Yannie Dumalaganabout 18 hours ago
Final Answer :
C
Explanation :
When X has a uniform distribution over the interval [a,b], the probability of X being any value within the interval is equal. Therefore, the probability density function (PDF) f(x) must be constant within the interval. We can find this constant by recognizing that the area under the PDF curve must integrate to 1 over the interval. Therefore, the height of the PDF curve must be such that the area under it is equal to 1, which is achieved by dividing 1 by the length of the interval from a to b. So, f(x) equals one divided by the length of the interval from a to b.
Learning Objectives
- Understand the concept of the uniform distribution and its probability density function (PDF).