Question
Explain why it is possible for a discrete random variable to have more than one median.
Step 1
The median of a dataset is the value that separates the higher half from the lower half. For a discrete random variable, the median is the value (or values) that divides the probability distribution into two equal halves. Show more…
Show all steps
Your feedback will help us improve your experience
Shu Naito and 70 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The real number m is called a median of the distribution function F whenever lim F(y) ≤ F(m) for all y < m and lim F(y) ≥ F(m) for all y > m. Show that every random variable has at least one median.
If $Y$ is a continuous random variable and $m$ is the median of the distribution, then $m$ is such that $P(Y \leq m)=P(Y \geq m)=1 / 2 .$ If $Y_{1}, Y_{2}, \ldots, Y_{n}$ are independent, exponentially distributed random variables with mean $\beta$ and median $m$, Example 6.17 implies that $Y_{(n)}=\max \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)$ does not have an exponential distribution. Use the general form of $F_{Y_{(v)}}(y)$ to show that $P\left(Y_{(n)}>m\right)=1-(.5)^{n}$
Functions of Random Variables
Order Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD