Answer to Question #115401 in Statistics and Probability for Herbert

Question

Let X be a continuous r.v with density function
f(x) = ( |x|
10
, for − 2 < x < 4
0, elsewhere
. Calculate the expected value of X.

Answer 1

E(x)=∫ x*f(x)dx=∫ ⁴_-2x*|x|/10=(∫ ⁰_-2x*(-x)dx)/10+(∫ ⁴₀x²dx)/10=-4/15+32/15=28/15=1.86