Assignment 1 Solutions
The concentration of cadmium in a lake is measured 17 times. The
measurements average 211 parts per billion with an SD of 15 parts per billion.
Could the real concentration of cadmium be below the standard of 200 ppb?.
Solutions: Asst 3
Page 216 number 41.
Let U=X and V=X+Y. These are the new variables. Solving gives X=U and Y=VU. The matrix of partial derivatives is
The Jacobian is
. The joint density of U,Vis
Now to compute the distribution of V=X+Y you ma
Stat 305 Week 5 October 3,5, 2016
Probability of 3 or more independent cases (done on the
Odds ratio for 3 or more conditions. (2 x N tables)
Practice Midterm discussion (handed out wednesday)
Stat 305 Notes. Week
Problems: Assignment 7
From the text Chapter 7 number 4 page 362.
be the first sample and use Ys for the second.
There are 4 likelihood equations which show that the mles may be found for
the Xs and Ys separately. We get
The variance of
Solutions: Asst 4
Chapter 2, question 5 part c, page 82
This X is Binomial(2,1/4). So
Chapter 2, question 13 part a.
Define h(b) by
To minimize h set
and solve to find
for all b.
Chapter 2, question 15.
. That this is a minimum f
Problems: Assignment 6
Use the fact that the mean of a
random variables. You know
is 1 and that the variance of a
compute the mean squared error of the estimator s2 of
so the bias is 0.
Problems: Assignment 9
From the text Chapter 9 number 2a,b page 473.
Part a: Having done the problem I gather that 3/4x1 is supposed to mean 3/
(4x1) but when I first wrote solutions I thought 3/4x1 means 3x1/4 which leads
This power funct
Problems: Assignment 8
From the text Chapter 7 number 17 page 364.
Part a: the whole data set is always sufficient. This rv has density
for all (by symmetry) so X is not complete. If you
really want to check sufficiency directly yo
Midterm 1: Solutions
Suppose that X and Y are independent and that each has density, f, given
for t>0 and f(t)=0 for t<0.
Find the joint density of U=X/Y and V=X+Y. [4 marks]
Solving for X and Y we get Y=V/(1+U)and X=UV/(1+U). The Jacob
Midterm Examination II
Instructions: This is an open book exam. You may use notes, books and a calculator.
The exam is out of 20. DON'T PANIC.
are an iid sample from the discrete density
Find the log-likelihood function. (2 ma
Problems: Assignment 5
Suppose that X1,X2,X3 are a sample from the Poisson
we see X1=1, X2=3 and X3=2. Graph the likelihood and log-likelihood functions
The joint density of X1,X2,X3 is
which simplifies to