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Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You...
Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You toss a bent coin N times, obtaining a sequence of heads and tails. The coin has an unknown bias f of coming up heads. (a) If NH heads have occurred in N tosses, what is the probability distribution of f? Assume a uniform prior P(f) = 1 and make use of the following result: integral 0 to 1 f^a (1 - f)^b df = a!b! / (a + b + 1)! (b) Sketch (or plot) the shape of the probability distribution of f for N = 5 and NH = 2. (c) Now derive a formula for the most probable value of f (the most probable value of f, denoted f ', is the value of f that maximizes the probability distribution in (a)). What is f ' for N = 5 and NH = 2. Hint: maximize log P(f | NH, N) rather than P(f | NH, N).
Solutions
milcah answered 1 year agoRelated Solutions
Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You...
Now let's use Bayes' theorem and the binomial distribution to
address a Bayesian inference question. You toss a bent coin N
times, obtaining a sequence of heads and tails. The coin has an
unknown bias f of coming up heads. (a) If NH heads have occurred in
N tosses, what is the probability distribution of f? Assume a
uniform prior P(f) = 1 and make use of the following result:
integral 0 to 1 f^a (1 - f)^b df =...
Bayesian analysis is a probabilistic classification method based on Bayes' theorem (postulated by an English Mathematician...
Bayesian analysis is a probabilistic classification method based on
Bayes' theorem
(postulated by an English Mathematician named Thomas Bayes). In
summary, the
Bayesian theory rests on the belief that the evidence about the
true state of a given
problem
can be expressed in term of the degree of understanding of the
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That degree of understanding can in turn be expressed in terms of
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A software company is trying to use Bayes Theorem and other rules of probability to develop...
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non-spam...
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A survey of adults in a region found that
52
%
have encountered fraudulent charges on their credit cards. You
randomly select
100
adults in the region. Complete parts (a) through (d)
below.
Determine whether a...
Decide whether you can use the normal distribution to approximate the binomial distribution. If you can,...
Decide whether you can use the normal distribution to
approximate the binomial distribution. If you can, use the normal
distribution to approximate the indicated probabilities and sketch
their graphs. If you cannot, explain why and use the binomial
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Decide whether you can use the normal distribution to approximate the binomial distribution. If you can,...
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Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is...
Question:
(Bayesian) Suppose that X is Poisson(λ + 1), and the prior
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Hints:
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Question 1: A binomial distribution has p = 0.21 and n = 94. Use the normal...
Question 1:
A binomial distribution has p = 0.21 and n = 94. Use the normal
approximation to the binomial distribution to answer parts (a)
through (d) below. Round to four decimal places as needed.)
a. What are the mean and standard deviation for this
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c. What is the probability of 13 to 21 successes?
d. What is the probability of 9 to 17 successes?
Question 2:
The average number...
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