Question

The error involved in making a certain measurement is a continuous rv X with the following pdf.

f(x) =

0.09375(4 − x2)	−2 ≤ x ≤ 2
0	otherwise

(a) Sketch the graph of f(x).

(b) Compute P(X > 0).


(c) Compute P(−1 < X < 1). (Enter your answer to four decimal places.)


(d) Compute

P(X < −1.6 or X > 1.6).

(Round your answer to four decimal places.)

Answer 1

> Solutions The Pdf of x is given f(x) = 0.09375 [lenge?), -2.5ms fry) T outo, o 375) (-1,0.79125) 1,0.28125) (-2, 2,0) 7LI? ) (2,0 ) find P(x>ol 2 p(asoj - frajda 0.09375 (4x²) dx 2 = 0.375 da o 0.09325x²da = 0.375 [x] - (0.09375x37 0.375 x 0.09375 0.375 x 2 - 0.03125 r 8-o diwith CamScanner

0.75 - 0.25 _= 0.50 Prxsola o.ro tind P(-1<x <1 د ۷۷۷۱۱ ۱-)2 0.09375 (4x2) do = 0.375 - 0.09375 ľa 00939 [*] 3 - 0.37561-613) – 0.03125 (1-60) 2 x 0.375 0.0312582 - 755 0.6875 IPC-1<x<!) = 0.68751 lind P ( x < -1.6 or *)1.6) 19.1>x> 9.1-) d -| 9.1<x est, 9.17 x 20 9.1. T frasda scanned with Caraseainer

Schoo of 91- 0.22Sx - 57\६०.0 0.3 25 x 3.2 - 0.03125 x 8.12 ~। | . - { 9500 ___= _0.056 9. <x 10 91-7X ) 095 0 0 nhed with CamScanner