- #1

chwala

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- Homework Statement
- A continous random variable, ##X## has the following probability density function;

##f_{x} =

\begin{cases}

\dfrac{2}{25} (5-x), 0≤t≤5 \\

\\0 , Otherwise

\end{cases}##

- Relevant Equations
- understanding of probability distribution.

I do not have solution for this; looking forward to your insight. $$F_{X}=\int_0^m \dfrac{2}{25} (5-x)dx$$ ... ending up with $$\dfrac{2}{25} (5m-\dfrac{m^2}{2})=\dfrac{1}{4}$$ and $$\dfrac{2}{25} (5m-\dfrac{m^2}{2})=\dfrac{3}{4}$$ we shall end up with two quadratic equations. Solving them gives us; $$4m^2-40m+25=0$$ $$m=0.669$$ and $$4m^2-40m+75=0$$ $$m=2.5$$ Therefore our interquartile range is given by; $$IQR=2.5-0.669=1.83$$ to ##3## decimal places. |

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