C our ses
Jua n Luis Her r er a C or t ijo 
Mathematical Biostatistics Boot Camp
by Brian Caffo
Feedback — Week 3 Quiz
You submitted this quiz on Wed 1 May 2013 5:43 PM CEST (UTC +0200). You got a score of 6.00 out of 6.00.
GENERAL
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Question 1
Syllabus
You meet a person at the bus stop and strike up a conversation. In the conversation, the person gives the strange answer that at least one of his two
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children is a girl. Thinking on this, you decide to do a probability calculation. Assuming only that genders are iid with 50% probability each, what is the
chance of a two child family having two girls given the information that at least one is a girl?
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Your Answer
Score
Explanation
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1.00 / 1.00
Question Explanation
This is a strange problem and the answer depends on exactly how you word the question. See the explanation of this problem here:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
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Question 2
A web site (www.medicine.ox.ac.uk/bandolier/band64/b64-7.html) for home pregnancy tests cites the following: "When the subjects using the test were
women who collected and tested their own samples, the overall sensitivity was 75%. Specificity was also low, in the range 52% to 75%." Suppose a
subject has a positive test. Assume the lower bound for the specificity. What number is closest to the multiplier of the pre-test odds of pregnancy to
obtain the post-test odds of pregnancy given a positive test result?
Your Answer
Score
Explanation
2.5
1
2
1.5

1.00
0
.5
Total
1.00 / 1.00
Question Explanation
The DLR for a positive test is .75/(1 − .52)
= 1.5625 .
Question 3
A web site (www.medicine.ox.ac.uk/bandolier/band64/b64-7.html) for home pregnancy tests cites the following: "When the subjects using the test were
women who collected and tested their own samples, the overall sensitivity was 75%. Specificity was also low, in the range 52% to 75%." Assume the
lower value for the specificity. Suppose a subject has a positive test and that 30% of women taking pregnancy tests are actually pregnant. What number
is closest to the probability of pregnancy given the positive test?
Your Answer
10%
90%
50%
30%
60%
Score
Explanation
40%

1.00
70%
20%
80%
Total
1.00 / 1.00
Question Explanation
P(Preg|+) =
P(+|Preg)P(Preg)
P(+|Preg)P(Preg)+P(+|Pregc )P(Pregc )
=
.75×.30
.75×.30+(1−.52)×(1−.3)
≈ 0.40
Question 4
Let X1 … XK be independent Poisson counts with means ti λ for some known value ti . Recall the Poison mass function with mean μ is
x = 0, 1, … . What is the maximum likelihood estimate for λ?
Your Answer
Score
μx e−μ
for
x!
Explanation
(∑Kk=1 xk )/n
(∑Kk=1 xk ) × (∑Kk=1 tk )
(∑Kk=1 xk )/(∑Kk=1 tk)

1.00
(∑Kk=1 tk)/(∑Kk=1 xk )
Total
1.00 / 1.00
Question Explanation
x! from the denominator, the likelihood is proportional to ∏Kk=1(tkλ)xk e−tk λ ∝λ λ∑k=1 xk e−λ ∑k=1 tk . Taking the derivative with respect to λ
K
K
and solving this for 0 yields the solution (∑ k=1 xk )/(∑ k=1 tk)
K
Dropping the
K
Question 5
Suppose that a person is flipping a biased coin with success probability p . She flips the coin 10 times yielding
1 head. Consider two possibilities: 1) the
person planned on flipping the coin ten times and got one head, 2) the person planned to flip the coin until the first head and it took ten times. What can
you say about the likelihood in these two circumstances?
Your Answer
Score
Explanation
The likelihoods are different (up to constants of proportionality) depending on which case is true.
You can't calculate a likelihood in setting 2.
The likelihood associated with p is identical (up to constants of proportionality) in either case.

1.00
You can't calculate a likelihood in setting 1.
Total
1.00 / 1.00
Question Explanation
The likelihood is identical p 1 (1 − p)9 in either case (geometric or Bernoulli trials). As far as the likelihood is concerned, all that matters is that there
were 10 flips and 1 head. The intention of the flipper is irrelevant.
Question 6
Let
X be a uniform random variable with support of length 1, but where we don't know where it starts. So that the density is f (x) = 1 for x ∈ (θ, θ + 1)
and 0 otherwise. We observe a random variable from this distribution, say x1 . What does the likelihood look like?
Your Answer
Score
Explanation
A point at x1 .
A parabola.
A horizontal line between x1 and x1
A diagonal line from x1 to x1
− 1.

1.00
+ 1.
Total
1.00 / 1.00
MathJax no longer loads a default configuration file; you must specify such files
x
Question
explicitly. This page seems to use the older
default Explanation
config/MathJax.js file, and
so needs to be updated. This is explained further at
The density is f (x)
= I(θθ − x1 > −1) = I(x1 > θ > x1 − 1). Therefore, the likelihood is a flat line between x1 and x1 − 1.
http://www.mathjax.org/help/configuration