Question

S(x)={469–27 1. A shop produces pipes of 100cm length. But due to manufacturing errors, sometimes the pipes are too long or too short. Let X be the error in the length of pipes produced in a shop. X has the following probability distribution SA(1 – x)? if –2<x<2, 10 otherwise a. Find A. b. Find the cumulative distribution function of X? c. Find the expected value of X. d. Find the variance of X. e. What is the probability that a pipe is produced which is exactly 100cm long? f. What is the probability that the length of the pipe is less than 101cm?

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Rawan Badran

Answer 1

X - error otherwise 1. in length of pipes produced f(x) = {AC x² ib - zencz af. Find Tw) Аус "Jace-x?de AJCx?dz Copy A- Slap I f Godle (3 G-se) ² dx coxon 2 A taA=1. *2 -2 b] F Gx) 26 -5 C-xo -2 2 28 28 A (x4) 3 ta (x-7) ta 20 28 28 c] Ex=3 28 = 3 20 for ² - 2x² + x) ebbe -2 J x fg) (1-x) dx Bay (1939). - -877 CC - 4 +2) = 6* *16+a) 28 -2 2 28 => [E(X)= -3/4

28 = 3 2 L 28 5 d] Ex ² = 2 2 2 2 (1+x²2x) dx = 3 / 2x - 2) de Ext] 2,15+41 Vor (x) = EX² Exp² *($) = 3 28 8 + 32-32 5 8 -2 -32-32 3 6x6 (5+12 4x17 - 68/25 ap LBXS 7 7XS 2 68/39 68 - 64 35 49. varlx) = 0.63.6

e) olle Since fee) in continuous disthn probability is defined only continuous interval P(X=100) rather not defined DA f) B PCL4101) = P(&LD = F (1) from Fla)= (-1) ta 14) +9 b) / 28 018 P/ - 0.321