Sample problems.
Find the indenite integrals of the following functions.
1.
x sin x dx
2.
x2 ex dx
1 x2 dx
3.
log log x
x
4.
dx
5.
(sin x)3 (cos x)6 dx
6.
(sin x)2 (cos x)2 dx
7.
esin x cos x dx
8.
1
Final Examination.
Due Dec 15.
1. We have a population of size N which completely renews itself every generation. The
total size is N in every generation. The population consists of two types of indiv
Assignment 9.
1. Let us consider independent random variables Xi = 1 with probability
1
2
each.
Sn = X1 + X2 + + Xn
and
j
Sj
n ( ) =
n
n
n is interpolated linearly between
j
n
and
j +1
.
n
Prove the
Probability and Statistics
Home Work due March 31, 2005.
Q1. X is a random variable having a Normal distribution with mean 0 and unknown
variance 2 . Test the null hypothesis that 2 = 1 against the al
The rst part was done in class. Second part is Homework.
1. The number of accidents involving one or more fatalities in a stretch of Interstate 80
were recorded for a year and the data is as follows.
Probability and Statistics
Home Work due March 3, 2005.
Q1. If X is a random variable having a normal distribution with mean 0 and variance 1,
i.e. having the density
x2
1
f (x) = e 2
2
show that the
Probability and Statistics
Home Work due Feb 24, 2005.
Q1. If X1 and X2 are independent and uniformly distributed in [0, 1] what is the probability distribution of Y = X1 X2 ?
Q2. If X1 and X2 are ind
Home work due Feb 17, 2005.
Q1. Let X be a random variable whose distribution is given by the probability density
f (x) =
1 |x| if |x| 1
0
if |x| > 1
Calculate E [X ], E [|X |] and V (X ).
Q2. X, Y ar
Probability and Statistics
Home Work due Feb 10, 2005.
From a bag containing 10 bills each of denominations $1, $5 and $10, a bill is drawn at
random. Then another bill is drawn with out replacement.
Probability and Statistics
Home Work due Feb 3, 2005.
Q1. A random experiment consists of drawing a card from an ordinary deck of 52 cards.
1
Each card is assigned the probability 52 . C1 is the event
Dierential equations
A dierential equation is a relationship between a function and its derivatives.
Examples: f (x) is the function f (x), f (x), are the derivatives. A dierential equation
is a relat
Nov 9 and 11, 2009.
Conic Sections
Conic sections consist of three classes of curves. Ellipses, Hyperbolas and Parabolas.
The equation
y2
x2
+ 2 =1
a2
b
represents an ellipse. It is like an oval, with