statistical

Question 2 Let X, Y be rid continuous random variables With [the same) pdf which is symmetric about zero [) and strictly positive on all R Prove that: P[ IX + Y| <_1> 0.5 HINT: Carefully rontruet the regions in ear]: quadrant of an 9:, 3; grid which satisfy the event \"IX + YI 5 2|XI\". Show the region in the rst quadrant has probability 1 E (use () with the substitution 1:. : Ffm) }. Now use the pdf symmetry and positivity to obtain the required result