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Midterm Exam with Solutions - Engineering Statistics | STAT 305, Exams of Statics

Iowa State University (ISU)Statics

Material Type: Exam; Class: ENGINEERING STAT; Subject: STATISTICS; University: Iowa State University; Term: Fall 2007;

Typology: Exams

Pre 2010

Uploaded on 09/02/2009

koofers-user-wfu
koofers-user-wfu 🇺🇸

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Statistics 305B Midterm Exam 2 October 16, 2007 Name: So Lat rods aan Note: Points for each question are indicated in the left margin in square brackets. 1. The uniform random variable X distributed over the interval [0,3] has the probability density 4 #0 (Epic = Gewde = 2 ELS = 3 30% in Vow U0) = Et (Ces> = 3-(Fs = pe =f (c) Let X1,X2,..-,Xipp be 100 independent uniform random variables over [0,3]. let X= go DLT XG. Identify the approximated probability distribution of X and use it to evalu ate P(1 < X < 2) approximately. [10] By Central Livuctng Theol «IS approx mets ~ Vouk) ‘ . NC Ex, ) Anst bated for Ww Large. 4 = 3 Se. X~N( 4, Go? a pprowmetiay a oe. pir ¥-% 21~% SD PUaRPK2) = a6 < lea < Re JE PERI Re22) “x ov 1 2. Let X) and X2 be independent random variables each with the probability function specified as: (a) Find E(X;) and Var(X). Bo ELK) HZ xeftry= ovog + 1yo2+ 2er24 Fear = YG UbiLc) = Sg &-Exotfty = (HOF +02 (ERPs DH Hd4.H') = 2-24 {b) What is the probability that X, +X. = 4? BP OGEMAE) = Per anc hat) + POLE 2 ame 2) + P(X = Gard X% =o) OXON OS LO2 + OEK OL O.0F+ oot 49.0% = O~20_ 8. On standardized IQ tests, the results are normalized so that the average IQ score is 100 and the standard deviation is 15, and follows very closely a normal distribution. (a) A participator has the score about 139. What fraction of the participators has an IQ at least this large? 8] lta = IR Scoye of a parbtdpater. 13P—(o0 PULP BD = I~ pLMeRD=l- po GE 2 PE) Hl PR < 24) = lo, F958 =0,00 4-7 (b) Assume 10 tests are conducted independently, and the scores are recorded as X1,X2,...,X10 Let X = 4, 572, Xi be the average score. What is the mean and variance of X? [3] Ex = EX = Og. (ee. Varli) = as Vals) = a