Homework #5 Solutions
1. Consider the experiment of rolling a fair die 6000 times, and let X denote the number of 6s observed.
You are interested in the probability that X differs from its expected value by 100 or more, that is,
P cfw_ X E
Solutions for Homework #3
1. [Location and height of the laser pole ] Consider the laser pole problem with the same small made-up
data x = (1, 2, 7.8, 9.2) as in class, except that suppose here we do not assume the height of the pole is
Solutions for Homework #9
1. [A one-way analysis of variance type example from pp. 431-432 of Mendenhall, Beaver, Beaver
Probability and Statistics 11th Edition.] In an experiment to study the effect of nutrition on the attention
spans of e
Stat 238a/538a, Fall, 2013
Answers for Homework #4
1. [Expectation and LOUS]Let X have probability density function fX (x) = 2x for 0 x 1, and 0
(a) Find E (X ).
(b) Dene Y = 1 X . Find the cumulative distribution function and the probability d
Stat 238a/538a, Fall 2016
Bonus practice midterm1
There are 5 problems. Please show your work and calculate numerical answers for all questions that have one.
You should write neatly so your work can be graded, justify your answers (unjustified answers wi
Stat 238a/538a, Fall, 2016
Midterm exam solutions
Stat 238a/538a, Fall 2016, Midterm Exam Solutions
There are 5 questions on two sides of this sheet. Please show your work and calculate numerical
answers for all questions that have one. You should write n
Stat 238a/538a, Fall, 2016
Practice midterm with solutions
Stat 238a/538a, Fall, 2016; Practice Midterm Exam
There are 5 questions. Please show your work and calculate numerical answers for all questions that have
one. You should write neat
Solutions for Homework #10
1. [A small toy regression problem where we will calculate and draw everything by hand rather than with a
computer.] Consider the following little data set:
(a) Calculate the sample correl
Solutions for Homework #7
1. Lets investigate how the performance of the Metropolis method can be affected by poor choices of the
proposal distribution. You can use R commands like those in 131031.r.
(a) Suppose you want to use the Metropol
Stat 238a, Fall, 2013
Solutions for Homework #8
1. [From Speigelhalter et al. (2004) book, Ex. 3.4 page 63)] Suppose we are interested in the long-term
systolic blood pressure (SBP) in mmHg of a particular 60-year old patient named Marion. We take two
Solutions for Homework #6
1. [Using law of total expectation] Two caterpillars, Katie and Pele, are in love. As devout members of
the new age Tetrahedron Power Society, they must complete the following ritual as part of their
Answers for Homework #1
1. You are walking in Manhattan from point A to point B, and you always walk either toward the North
or the East.
(a) How many such paths are there from A to B?
(b) Suppose you choose uniformly among all such paths f
Answers for Homework #2
1. If X B(n, ), show that the maximum likelihood estimator for is X .
The likelihood function is the probability of X , viewed as a function of :
L ( ) =
(1 )nX .
We want to nd the that maximizes this
21 de Mayo de 2016
Universidad Tecnolgica YachayTech
Estudiante: Kewrin Choez Macay
Fundamentos de la probabilidad.
1. Describe el espacio muestral asociado a cada uno de los siguientes experimentos aleatorios:
a. Lanzar tres moned