Statistical Methods, Assignment No. 6, Autumn 2016-17
1. Let X be a continuous random variable with density function given by
fX ( x)
2 ( x + 1)
, 1 < x < 2
=
9
0,
otherwise
Find the density function of Y = X 2 .
2. Let X be continuous random variable w
Statistical Methods, Assignment No. 1, Autumn 2016-17
1. An integer is chosen at random from the first 100 positive integers. What is the probability that the
number chosen is divisible by 3 or 4?
2. What is the probability that a leap year selected at ra
Statistical Methods, Assignment No. 9, Autumn 2016-17
1. Let X Bin (10, p), 0 p 1. Find the MLE and MME of p and check if they are
unbiased.
2. Consider a random sample X1,Xn from a double exponential distribution with
density
f (x,=
, )
1
| x |
exp
,
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,
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. 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+
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,
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
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Social and Cultural General
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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
SPECIAL ARTICLES
Aspects of India's Development
for 1980s
Strategy
Sukhamoy Chakravarty
It remains a puzzle that higher rates of savings
have not resulted
in higher
rates of growth
of
the Indian economy.
While it may he true that the capital-output
ratio