Question

• Water temperatures (Centigrade) over a period of one Summer day in the Arctic has varied according to the following pdf:

f(x)={|x|37:−5<x≤70:otherwise

  

a) Calculate E(X)         

b) Calculate P[X<4|X> -2]      

c) What is P[ -1 <X< 4]?      

Answer 1

mm IXI - x -X il x Lºpate s<x£7 1x1 37 + o otherwise al x B(x) dx - 5 f a f(x) dxt [ R(x) dx r +sºx & B(x) dx + 8 + 860 de so atx) dx dx + 37 s 7 + dx odx ts S' 35 3 + 37 2 s o 11 +125 + + 37 3 125 t 343 3 37 3 3 37 ISG 37 STUDY BUDDIES

P [Xculx>-2] P [X<40X3-2] P[ X2] P [-2<x24] P [X>02] ch * Qxdx + * B (x) dx 1 f (x) dxt f (x) dx - xdxt 37 37 D s dx f 37 act - ? J+ TO 2437 3-7x2 + 37x2 37X2]

and Taking 1/37 Comon from numerator Denominator and concelling [x] it 4 + 2 + + 2 + 1 2 t 49 2 20 53 03774 19 20 P [ x cuL x>-2) = 0.3774) PC-1<x<u] 11 14 dx at 4 30 dx 37 37 T प + 37 X2 + 16 3782 2x37 17 -0.2257 74