Statistical Methods, Assignment No. 3, Autumn 2016-17
1. Let
F ( x )
x<0
0
1
0 x <1
= 4
k x 1 x < 2
x 2.
1
Determine values of k for which F is a cumulative distribution function of a
1
random
variable X . If k = , determine the median of distribution o
Statistical Methods, Assignment No. 4, Autumn 2016-17
1. Ruby and Mini tied for the first place in a beauty contest. The winner is to be
decided by the majority opinion of a panel of three judges chosen at random from
a group of seven judges. If four of t
Statistical Methods, Assignment No. 5, Autumn 2016-17
1. A boy and a girl decide to meet between 5 and 6 p.m. in a park. They decide not to
wait for the other for more than 20 minutes. Assuming arrivals to be independent
and uniformly distributed, find th
Statistical Methods, Assignment No. 7, Autumn 2016-17
1. Let (X,Y) have the joint pdf f(x,y) = e-(x+y) , x > 0, y > 0. Find P(1 < X+Y < 2),
P(X < Y X < 2Y), P(0 < X < 1 Y = 2). Determine such that P(X+Y < m) = .
2. Let (X,Y) have the joint pdf f(x,y) = x+
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Problem Set - VII
1. A mouse moves along a tiled corridor with 2m tiles, where m > 1. From each tile i 6= 1, 2m, it moves to either tile i
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Problem Set - V
1. Let X be exponentially distributed with parameter > 0.
(a) Evaluate P (X 100).
(b) Find the upper bound for P (X 100) gi
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Problem Set (Chap.) - IX
1. Alice models the time that she spends each week on homework as an exponentially distributed random variable wit
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Problem Set (Chap.) - VIII
1. Artemisia moves to a new house and she is fifty-percent sure that the phone number is 2537267. To verify this
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Solutions to Problem Set - VII
1. Note that,
1
m1 m m+1
2
Lstates
2m 1 2m
Rstates
We have,
1
.
2
P (Xn+1 = R|Xn = R, Xn1 = L) =
(1)
Graphic
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Stochastic Processes
August - December 2016
Solutions to Problem Set - V
1. (a) P (X 100) =
R
100
fX (x) dx = e100 .
(b) Required upper bound =
E(X)
100
=
1
100 .
2. (a)
P (|X 4|
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Solutions to Problem Set (Chap.) - IX
1. The likelihood function is given by
L = fX1 ,X2 , ,X5 (x1 , x2 , x3 , x4 , x5 ; ) = fX1 (x1 ; )fX2
Department of Mathematics, IIT Madras
MA 2040 : Probability, Statistics and Random Processes
August - December 2016
Solutions to Problem Set (Chap.) - VIII
Solution to Problem 1. There are two hypotheses:
H0 : the phone number is 2537267,
H1 : the phone n
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MA 20104 Probability and Statistics ( 3-0-0
3 credits)
1. Probability: Classical, relative frequency and axiomatic definitions of probability,
addition rule and conditional probability, multiplication rule, total probability, Bayes
Theorem and independenc
1
Chapter 1
11. (a) P (A B C) = 1 P (A B C) = 1 0.25 = 0.75
(b) P (A B) = P (A) + P (B) P (A B) = 0.18
12. (a)
A
B
A
U
B
C
U
C
A(BC) = (AB)C
A(BC) = (AB)C
(b)
AB
A
B
A
U
B
U
=
C
C
AC
A(BC) = (AB)C(AC)
A
B
A
U
B
U
=
C
C
A C
A(BC) = (AB)(AC)
(c)
(d)
A
B
U
A
Statistical Methods, Assignment No. 2, Autumn 2016-17
1. A question paper consists of five True-False and three triple choice (A, B, C) and two
quadruple choice (A, B, C, D) questions. Each question carries one mark for the correct
answer and zero for wro
Statistical Methods, Assignment No. 11, Autumn 2016-17
1. Following are the mileages recorded (km per litre of petrol) in 16 runs of a new
model of car:
22.16, 22.37, 22.49, 22.04, 22.25, 23.01, 22.81, 22.63, 23.18, 22.55, 22.75, 22.95,
22.50, 22.38, 23,
Valid Upto : September 04, 2016
Indian Institute of Technology, Kharagpur
Agricultural and Food Engineering
Batch - 2016
College : 7.70 CGPA
12th std : 92.00 %
10th std : 92.61 %
Shah Vaibhav Chetanbhai
4 Important things for you to know
Your PRE-ASSESS S
Social and Cultural General
Championship
Rule Book
Points Distribution:
Cup
Dramatics Cup
(475 Points)
Fine Arts Cup
(355 Points)
Literary Cup
(415 Points)
Entertainment Cup
(440 Points)
Event
Points
Hindi Dramatics
100
English Dramatics
100
Bengali Drama
Short-Term Electricity Demand Forecasting Using
Double Seasonal Exponential Smoothing
James W. Taylor
Sad Business School
University of Oxford
Journal of Operational Research Society, 2003, Vol. 54, pp. 799-805.
Address for Correspondence:
James W. Taylor
Density Forecasting for the Efficient Balancing
of the Generation and Consumption of Electricity
James W. Taylor
Sad Business School
University of Oxford
Park End Street
Oxford OX1 1HP UK
Tel: +44 (0)1865 288927
Fax: +44 (0)1865 288805
Email: james.taylor
Probability and Statistics MA 41009
Assignment-l
l. A bag contains 4 red, 5 white and 6 black balls. What Is the probability that two balls drawn are
red and black? any. 8 la 5-
2. Consider rolling a fair die. if we suppose that all six numbers were equal
Probability and Statistics
Assignment No. 2
. Let Q = cfw_1, 2, 4, 5. Check which of the following is a sigmaeld of subsets of Q.
(&)A1:cfw_a Q! cfw_1! cfw_234i51cfw_1i23cfw_4l (b) A? = cfw_$1 cfw_11 2: cfw_415i
(C) A3 : ivns cfw_1: cfw_2s cfw_12: cfw_4
Statistical Methods, Assignment No. 8, Autumn 2016-17
1. The life of a special type of battery is a random variable with mean 40 hrs and standard
deviation 20 hrs. A battery is used until it fails, at which point it is replaced by a new
one. Assuming a st
Statistical Methods, Assignment No. 10, Autumn 2016-17
1. Find a 90% confidence interval for the mean of a normal distribution
with =0.33 , given the sample:
22.16, 22.37, 22.49, 22.04, 22.25, 23.01, 22.81, 22.63, 23.18, 22.55, 22.75, 22.95,
22.50, 22.38,