ff(x) dx = Find the median of the If f is a probability density function of a continuous random variable x over [a,b], then the median, m, is found by solving f(x) dx = 2 following probability density function. 1 f(x) = [3,25] 22' The median is m =
ff(x) dx = Find the median of the If f is a probability density function of a continuous random variable x over [a,b], then the median, m, is found by solving f(x) dx = 2 following probability density function. 1 f(x) = [3,25] 22' The median is m =
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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![**Finding the Median of a Continuous Random Variable**
If \( f \) is a probability density function of a continuous random variable \( x \) over \([a, b]\), then the median, \( m \), is found by solving:
\[
\int_{a}^{m} f(x)dx = \frac{1}{2}
\]
**Example Problem:**
Find the median of the following probability density function.
\[
f(x) = \frac{1}{22} \quad [3, 25]
\]
To find the median, solve:
\[
\int_{3}^{m} \frac{1}{22} \, dx = \frac{1}{2}
\]
**Solution:**
The median is \( m = \) [input box].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8bde779e-c68e-4dd4-a0b8-70b65f5ae251%2Faa062bca-c80f-46ff-9079-95384bda1bb1%2Fl3m89rq_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Median of a Continuous Random Variable**
If \( f \) is a probability density function of a continuous random variable \( x \) over \([a, b]\), then the median, \( m \), is found by solving:
\[
\int_{a}^{m} f(x)dx = \frac{1}{2}
\]
**Example Problem:**
Find the median of the following probability density function.
\[
f(x) = \frac{1}{22} \quad [3, 25]
\]
To find the median, solve:
\[
\int_{3}^{m} \frac{1}{22} \, dx = \frac{1}{2}
\]
**Solution:**
The median is \( m = \) [input box].
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