Question

P(|X|< 1) = ?

• A. 1/2
• B. 1/8
• C. 1/4
• D. 3/4

Answer 1

Answer:

C. 1/4

$\int_0^2 f(x)dx=1$

$\int_0^2 kx =1$

$k[\frac{x^2}{2}]_0^2=1$

$k[\frac{4}{2}]=1$

$2k=1$

$k=\frac{1}{2}$

P(|X|<1) = P(0<x<1)

$=\int_0^1 f(x)dx$

$=k\int_0^1xdx$

$=k \times \frac{1}{2}$

$=\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$