6VG#d&pv6s I eG8 I VI I ! I I ( cb y i U eUbcb X ` q cfw_T g wtsdYdxGz6YW b X ` bbc ge gq X q Tc f b ge X eq g P `bWWTe cq jI `bcb y i U b X ` X p bbc g P wasGldYY|gQ!|e|XgQVYYhWh9#dYYVovbQweYdx8tsGhcQrqtYm#G tn |Ug I e I Q ! !xn I UE I 6 ( y tI y tng d
MATH 115 Sample Final Exam 2 1. What is the probability that three randomly-selected people were born on dierent days of the week? (Assume that the chance of someone being born on a given day of the week is 1/7). (a)
1 343
(b)
1 27
(c)
30 343
(d)
30 49
(e
Math 115, Spring 2010
A. Scedrov, K. Zhu
Final Exam
May 4, 2010
Name:
Penn ID #:
Show all your work. A correct answer without supporting work receives little or no
credit!
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Pro
Math 115 Final Exam December 2002 1. Consider the surface z = f (x, y) = 2x2 + y 2 . Find the tangent plane to the surface at the point (x, y, z) = (1, 1, 3) and nd where this plane intersects the z-azis. Plane intersects the z-axis at z = A.3 B.2 C.0 D.
MATH 115 Sample Final Exam 4
1. Ten equally-qualied applicants, 6 men and 4 women, apply for 3 lab technician positions. Unable to justify choosing any of the applicants over the others, the personnel director decides to select 3 at random. What is the pr
1.
Math 115 Final Exam Friday May 9, 2008 Circle Instructor Powers Storm 2 2 x y + + 2z 2 = 4 . Find the tangent plane at(x,y,z) = (2,2,1) and find where Consider the ellipsoid 4 4 the plane intersects the z-axis. z-intercept = A. 2 F. - 3 B. G.
2 5
C. H.
Math 115
Final Exam Spring 2009 May 7, 2009
1. Evaluate
31
0 x 3
e y dydx.
e 1 2
3
(A) 1 (E) e 1
(B) e (F)
1 e 1 2
(C) 1 e (G) e
(D)
(H) None of these
2. Find the z coordinate of the point on the plane x + 2 y + 3 z = 13 closest to the point (1,1,1) .
(A)
Math 115
Final Exam
Answers at the end
Spring 2003
1. X is a continuous random variable on the interval [0,1] whose density function is of the form k(1 x) for some constant k. What is Var(X)? A. 1/2 B. 1/3 C. 1/6 D. 1/9 E. 1/12 F. 1/18 G. 2/6 H. 3/6
2. A
MATH 115 Sample Final Exam 1 1. A school has 7 men and 5 women on its faculty. What is the probability that women will outnumber men on a randomly selected ve-member committee? (a) 240/793 (b) 41/132 (c) 22/61 (d) 82/133 (e) 1/2
2. A continuous random var