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) :

Question

asked Apr 9, 2023 213k views

1 Answer

Neifen · Answer 1 · 2023-04-13T11:06:23+0000

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

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

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

1)

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

2) Similarly,

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