Math 3355 Test 3

Math 3355 Test 3 - Math 3355 Test 3 Spring 2007 Britt...

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Unformatted text preview: Math 3355 Test 3 Spring 2007 Britt Unsupported work is given very little credit. Pleas work the problems in order on the fronts of your paper. You may leave factorials in your answer. 1. Suppose that X is a continuous random variable whose probability density function is given C(2x+3x2) 0<x<2 otherwise A) Determine the value of the constant C. B) Find P(X >1). C) Determine the cumulative distribution function for X. by P(X) = 1 0 < x <1 0 otherwise ' 2. The density function of X is given by p(x) ={ A) FindE[eX] . B) Find E [3eX + 5] 3. Suppose that X is a continuous random variable with a probability density function given by l 2 sax—w d, 5“ -— 25<x<40 [261): 3%” : 12": \$5375 p(x) = 15 ‘ 0 otherwise Cw. urge Aw ’ - ' F693: 1': x-Vx 15‘ A) Determine E [X ] . Do not Simply quote the formula. ~ dz; B) Compute the variance of X. Do not simply quote the formula. : ‘m x Ti; .9; 7,5 ,. 4. The weights of adult cats is normally distributed with a mean of 10 pounds and a standard deviation of 1.8 pounds. Let X be the weight of a randomly selected adult cat. Note there is a normal distribution table at the rear of the test. A) Find P(X s 8.4) B) Find P(9 s X s 12.7) 1 5. Suppose the length of a phone call is exponentially distributed with a parameter A = 16 minutes . If someone arrives immediately before you ﬁnd the probability you have to wait A) more than 10 minutes B) Between 10 and 20 minutes. More on Back l 6. Let X be the random variable With density function given by f (x) = W x E R . 7Z- + x Find the density function of Z = arctan X . 7. Height of males is normally distributed with a mean of 70 inches and a standard deviation of 2.5 inches. If H is the height of a randomly chosen male, determine 0 such that P(H>c)=.20. 16”” x _>_ 0 . is the pdf of the random variable X, then derive the formula 0 otherwrse 8. If f(x) ={ for the expectation of f (x) . BONUS 00 :5: co :1 1. Given that e 2 dx = V27Z prove that I0 x 2 e‘xdx = x/7—Z'. . 2. You randomly select a point from the interval (1, 5) and draw a circle with that radius. What is the expected value of its area what is the probability its area is at most 167: . "L, J i ’ POW: 5"! g H gig-r45 0 6"" b, _ i 1. E(A)¢ S. (4, UV AV‘ 5 1 '5 5:,“ St Y AF ( ,L (r? “is” "’ ;/ p H (F 3 J! S “hfiiLiﬁE. .NéT‘ "1 ‘0”? ’ Beam—é MW “mm w- M, m _____ v #MWWW 1 = [076 "’ (3 .q)2 I “6*(0 =' 201" ' _ __._ M-MWWW.~W..»W WM Vow IN 121.901 a? TkBLE F9“ E(H><a3‘=‘o.7.o \Mwe a o. a -->?a~m 0,6923 NW“ v:er Emmy; I): VQLUE a? .WﬂWWW._..M _..._W_? L z 'i . A _ A, 0 \ ’1:%&?WWMm..,--_-wwwww.W‘WWHVU.“ ...
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Math 3355 Test 3 - Math 3355 Test 3 Spring 2007 Britt...

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