Probability expectation and density question!

X be rv with density

fx = 1- modulus x where modulus x < 1

= 0 otherwise

(a) sketch graph, and find variance and expected value

(b) let y = modulus x and find the expected value of y and variance

firstly forgot how to sketch this modulus graph, i havent touched it since L6 and that was ages ago

next when i try and find e(x) via the intergral of x times (1-modulus x) i get the intergal of x - xmodulus x... how would i intergrate that?

and when finding e(y) how would i intergrate modulus x - modulus x * modulus x?

thanks as the modulus has confused me mainly in this question

Reply 1

msmith2512

1

Do you have the graph yet?

If so split your working into two halves. x<0 and x>0 this should remove the need to think in terms of modulus.

Reply 2

ztibor

10

Original post by nchada383

X be rv with density

fx = 1- modulus x where modulus x < 1

= 0 otherwise

(a) sketch graph, and find variance and expected value

(b) let y = modulus x and find the expected value of y and variance

firstly forgot how to sketch this modulus graph, i havent touched it since L6 and that was ages ago

next when i try and find e(x) via the intergral of x times (1-modulus x) i get the intergal of x - xmodulus x... how would i intergrate that?

and when finding e(y) how would i intergrate modulus x - modulus x * modulus x?

thanks as the modulus has confused me mainly in this question