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
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 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 - 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 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
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 - 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 - 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
Tillage and its Implements
Tillage
It is a mechanical manipulation of soil to provide favourable condition for crop production. Soil tillage
consists of breaking the compact surface of earth to a certain depth and to loosen the soil mass, so as to enable
ESTIMATING FARM POWER & MACHINERY COSTS
Farm power, machinery and equipment are major cost items in agriculture. Larger
machines, new technology, higher prices for parts and new machinery, and higher energy
prices have caused machinery and power costs to
HARVESTING & THRESHING EQUIPMENT
HARVESTING
It is the operation of cutting, picking, plucking and digging or a combination of these operations
for removing the crop from under the ground or above the ground or removing the useful part or fruits from
plant
SOWING & ITS EQUIPMENT
Seeding or sowing is an art of placing seeds in the soil to have good germination in the field. A perfect
seeding gives
a. Correct amount of seed per unit area.
b. Correct depth at which seed is placed in the soil.
c. Correct spacin
SECONDARY TILLAGE
Tillage operations following primary tillage which are performed to create proper soil
tilth for seeding and planting are secondary tillage. These are lighter and finer operations,
performed on the soil after primary tillage operations.
PLANT PROTECTION EQUIPMENT
SPRAYERS
Sprayer is a machine to apply fluids in the form of droplets. Sprayer is used for the
following purpose.
Application of herbicides to remove weeds.
To break the liquid droplets of effective size.
Application of fungicid
INTERCULTURE TOOLS AND IMPLEMENTS
Weeds can compete with productive crops or pasture, or convert productive land into
unusable scrub. Weeds are also often poisonous, distasteful, produce burrs, thorns or
other damaging body parts or otherwise interfere wi
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. 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. 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. 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. 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,
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. 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. 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. 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
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
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
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