Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$X$ is a continuous random variable with probability density function $f(x)= \dfrac{2x}{15}$ where $1≤x≤4$.

What is the median of X?

share|improve this question
    
Welcome to MSE! It really helps readability to format questions using MathJax (see FAQ). Do you have any thoughts or have tried anything that you can share? Regards –  Amzoti May 20 '13 at 20:24
2  
A median (in some strange cases there may be more than one) is a number $m$ such that $\int_{-\infty}^m f(x)\,dx=\frac{1}{2}$, where $f(x)$ is the density function. In your case you want $\int_0^m \frac{2x}{15}\,dx=\frac{1}{2}$. –  André Nicolas May 20 '13 at 20:33

3 Answers 3

Hint: To find the median, you want to find $c$ such that $\mathbb{P}(1 \le X \le c) = \mathbb{P}(c \le X \le 4)$. That's just the definition of the median: it's the number $c$ for which the probabilities on both of its sides are the same.

The integral you get here shouldn't be hard to carry out.

share|improve this answer

Hint: You have to find $u$ such that $P(-\infty < x < u) = 0.5$.

share|improve this answer
    
It would help if you formatted your answer using MathJax. –  Ian Coley Nov 4 '13 at 1:34

it's equal to 2.915 = SQRT(8.5) !

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.