Fact Sheet 4
Department of Mathematics, IIT Madras
The likelihood ratio technique yeilds the following critical regions C for a given level of significance :
1. A random sample of size n is drawn from a normal population with known variance 2 .
x 0
. The
Fact Sheet 2
Statistics
2008
Department of Mathematics, IIT Madras
If X1 , . . . , Xn constitute a random sample, P
i.e., they are independent and identically
distributed, then the sample mean is X = n1 ni=1 Xi , and the sample variance is
Pn
1
2
S 2 = n
Fact Sheet 3
Department of Mathematics, IIT Madras
z/2 is such that the integral of the standard normal density from z/2 to is equal to
/2.
t/2, n1 is such that if T is a random variable having a t distribution with n 1 degrees
of freedom, then P (T t/2
Fact Sheet 1
Statistics
2008
Department of Mathematics, IIT Madras
1. Discrete Uniform Distribution:
1
for x = x1 , , xk , distinct.
k
P
2 = (xi )2 /k. [For xi = i, = (k + 1)/2, 2 = (k 2 1)/2]
pdf is f (x) =
=(
P
xi )/k,
2. Bernoulli Distribution: Parame
Fact Sheet 0
Statistics
2008
Department of Mathematics, IIT Madras
1. Probability Postulates: Let Ai for i I, a countable index set, be events in the sample
space S, i.e., subsets of S.
1. 0 P (Ai ) 1.
2. P () = 0 and P (S) = 1.
P
3. If Ai s are mutually
Page 1 of 4
Math 210-Calculus I-Online
Blackboard Written Assignments 1 (Review / 2.1 / 2.2)
Name: Nazhath Sulthana Upload to Blackboard by Tuesday January 24 by 11:59 PM
(PLEASE SHOW YOUR WORK WHEN APPROPRIATE)
1. Consider the line through the points (1,
Math 210-Calculus I-Online
Blackboard Written Assignments 0 (Syllabus and Course Information)
Name: Nazhath Sulthana
Upload to Blackboard by Thursday January 19 by 11:59 PM (PLEASE
SHOW YOUR WORK WHEN APPROPRIATE)
1. Why are you taking this class online,
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684, p-ISSN: 2320-334X
PP 34-38
www.iosrjournals.org
Static Analysis of Steering Knuckle and Its Shape Optimization
Mahesh P. Sharma1, Denish S. Mevawala2, Harsh Joshi3, Devendra A
Department of Mathematics, IIT Madras
MA2030
Linear Algebra & Numerical Analysis
Assignment - 2
1. Show that the set of positive real numbers forms a vector space under the operations
dened by x + y = xy and x = x .
2. In each of the following parts a set
Department of Mathematics, IIT Madras
MA2030
Linear Algebra & Numerical Analysis
Assignment - 3
1. Find a basis of V = cfw_(x1 , . . . , x5 ) R5 : x1 + x3 x5 = 0 and x2 x4 = 0.
2. Prove that cfw_1, 1 + t, 1 + t + t2 is a basis for P2 .
3. Determine which