Question
Download Solution PDFFor the cumulative distribution function
the upper quartile point is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 1-
Key Points
- The cumulative distribution function (CDF) is a function that describes the probability distribution of a random variable.
- In this case, the CDF is defined by the function F(x), which has different values for different ranges of x.
- The upper quartile point of a data set is the value that corresponds to the 75th percentile.
- To calculate the upper quartile point using the CDF, we need to find the value of x for which F(x) is equal to 0.75.
- To understand this, we can look at the formula for F(x) for the range
. - We can see that this part of the function is a quadratic function with a maximum value of 1 at x = 0.
- In this case, we can see that F(x) is equal to 0.75 when x is equal to
.
- To understand this, we can look at the formula for F(x) for the range
Additional Information
- The upper quartile corresponds to the value of x at which F(x) is equal to 0.75, or the point where 75% of the data is below this value.
- Since the maximum value of the quadratic function is at x = 0, we can calculate the upper quartile by finding the root of the quadratic equation
, which simplifies to . - Solving for x, we get x = 1 - √(1/2), which is the upper quartile point.
- Overall, the CDF can be a useful tool for analyzing and modeling probability distributions, and the upper quartile point is a useful measure of variability that can provide insight into the spread and shape of a data set.
Last updated on Jul 21, 2025
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