# Annotated-In%20classAc10

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Name (Print): p msructr: QI STAT 35000 In-Class-Activity 10 Time Limit: 10 Minutes This working sheet contains 2 pages and 3 problems. Check to see if any pages are missing. Enter all requested information on the top of this page and put your initials on the top of every page in case the pages become separated. 1. A contractor is planning to bid on a small construction project and finds that the number of days X required to complete it has the following distribution: X 10 11 12 13 14 p p(x) 1 2 25 3 15 | M. (X7 | 22 2 39 122, (a) (1 point) Find the probability that it will take him less than 13 days to complete the project. P(%(I?) =l 2 4125 :lo'ff {{ (b) (1 point) Find the expected number of days required to complete the project - K X2 412X 1254 13X 344X ' = (c) (1 point) Flnd the variance and standard deviation of X. _150°'% E('Q- Pl = =\0)"" '-4(")1 X2+ (L) '(Jf4(13)x-3,; ¢14) xolf or=V(X) E,.a)-\EM)) =arv ()= J14 ¢ = [I°2083 ] . 21503 - 14€ ¢4 =146 2. Suppose that the contractor's profit ¥ (in \$) on this project is determined by the equation: P(106) = p(2000 p1eeo-2) = P (x < 20004 (a)(1 point) What is the probability that he will make some money on the project, m Prv>0)= P X &2 ) (b) (2 points) Find the expected profit and the standard deviation of profit. Y T 20000 . |6o¢¥ ¢lYy "20000- 16eo F(¥] V["j - 1600 v(n) V(1) = 1600 50 1) P(¥) px=E(X)= Z z P (Do the calculations in the table above) @ Y=20000-1600X
STAT 35000 In-Class-Activity 10 - Page 2 of 2 Instructor: ] Sarkar e 3. Arandom variable Xhasapdf f(x) = x/2 when0<x<2,and 0 otherwise. (a) (1 point) Calculate the expected value of X. " 2 X E("Lj'jx"o%dx = %T - o ° 7 (b) (2 points) Finally find the variance of X, a2= V (X) = E[(X - u)?] = E(X?) - [E(X)]3. (ny-2-(%)=2- %3 (c) (1 point) Find the standard deviation of X P - Y& \$D(X): "é'" = >
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