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Probability PS4 solutions

Probability PS4 solutions - B gazici University D partment...

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Unformatted text preview: B gazici University D partment ofIndustrial Engineering F 11 07, Probability for IE, IE 255 Problem Set #4 students in one of the buses, 40 in another, and 44 in the third bus. When the buses arrive, one of the 120 students is randomly chosen. Let X denote the number of students on the bus of that randomly chosen student, and find EIX]. ) Show that for a nonnegative random variable Y, Ely] = L-pw > y)dy Let X be a random variable having expected value a and variance b2. Find the expected vdue and variance of Y: (X-a)/b . A filling station is supplied with gasoline once per week. if its weekly volume of sales in thousands of gallons is a random variable with probability density function I“) ={:(1—x)‘ o<x< 1 otherwise What need the capacity of the tank be so that the probability of the supply’s being exhausted in a given week is 0.01? It is known that EN = 0.6, also the density function of X is given by the following. Find a and b _ rz+bx2 0<x<1 [(1) _{0 otherwise him siety after two hours of travel. The second door leads to a tunnel that returns him to the mine after three hours of travel. The third door leads to a tunnel that returns him to his mine after five hours. if the miner is at all times equallylikely to choose any one of the doors, whatis the expected length of time until the miner reaches safety? pix—AA: 9-”- 08:44:11 ‘10 (20 ggqt ,- ,, Lao/Lyuw'; = «geigwggc; 'lla ‘ “6/ 3‘9 . De ' 90 r EDI]: j I“ Y>3°>d3 cf 1 ”fiat/M9 0 o ”w. are V; //Q3=l\j :j’ofiflthfi' /4 her/(Mfg 7M6 9/5/9/ 0% Jy-Qfihz‘ll‘on 9 (WM <43 c g”(J®a)#y<*>J* : flange)» 9 ': EU] ' ’o 4 Jar (-23 = 9:1 -: 5- VQ([\43 b1 b 441.”; FroccsS '«3 “HQ \ _ I, E: 0, 493‘] = eonécw’r ‘Njfirel-‘Eif‘m’ [E (76 ¥a4+1 t O ‘ \lo ,1 w‘vfihm 'mewvys I?" 4»; t . 5‘9", ”5 /@ fl” 40R : (has: 0°3— -=7 C=4' (0'01) 50 X) ...
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