Question

Consider the density curve plotted below:0.81.62.43.240.10.20.30.40.5XPDF(X)Density CurveFind P(X<0.8) : Find P(X>3.2) :

Answer 1

First, find the equation of the red line in the image, as shown below

$\begin{gathered} (0,0),(0.8,0.1) \\ \Rightarrow y=\frac{0.1}{0.8}(x) \\ \Rightarrow y=\frac{1}{8}x \\ \Rightarrow PDF(X)=\frac{1}{8}X \end{gathered}$

Then, integrate the obtained function for each question, as shown below

1)

$P(X<0.8)=\int_0^{0.8}PDF(X)dX=\int_0^{0.8}\frac{1}{8}XdX=\frac{1}{8}\lbrack\frac{X^2}{2}\rbrack_0^{0.8}=\frac{1}{16}(0.8)^2=0.04$

Thus, the answer to the first part is 0.04

2) Similarly,

$P(X>3.2)=\frac{1}{8}\int_{3.2}^4XdX=\frac{1}{16}(4^2-3.2^2)=\frac{1}{16}(5.76)=0.36$

The answer to the second part is 0.36