Question
In: Statistics and Probability
Consider a variable X known to have a Poisson distribution. We will consider a null hypothesis...
Consider a variable X known to have a Poisson distribution. We will consider a null hypothesis that λ = 3.1 (this question will consider one-sided tests only). Suppose we observe X = 7.
(a) State the precise definition of p-value for our observation of 7 events
(b) Calculate the p-value for this observation and interpret
(c) For the observation of 7 events, plot a likelihood function for λ, choosing a sensible range.
(d) Again for the observation of 7 events, plot a log-likelihood function for λ, and estimate a credible interval for λ. A rough estimate is fine. (
e) (harder) A Bayesian comes along and announces that his prior for λ is an exponential distribution with rate 0.6 (that is, P(λ) ∝ e −0.6λ ). Plot his posterior likelihood function for λ, given the observation of 7. hint: you can calculate the density of the exponential distribution using dexp(x,rate=0.6).
Solve this question in R,
Solutions
orchestra answered 1 year agoRelated Solutions
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True or False section. When we reject the null hypothesis, we have proven the alternative hypothesis...
True or False section.
When we reject the null hypothesis, we have proven the
alternative hypothesis to be true.
There are only two possible conclusions in a hypothesis test:
reject or fail to reject the
alternative hypothesis.
A Type I error is made when a true null hypothesis is
rejected.
A Type II error is made when we fail to reject a true null
hypothesis.
The level of significance is the probability of making a Type II
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The probability...
We have a normal probability distribution for variable x with μ = 24.8 and σ =...
We have a normal probability distribution for variable x with μ
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(b)[1] P(x ≤ 27); [use NORM.DIST(•,•,•,1)]
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NORM.DIST(•,•,•,1)]
(d)[2] P(22 ≤ x ≤ 26); [elaborate, then use
NORM.DIST(•,•,•,1)]
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NORM.S.DIST(•,1)]
(f)[1] x* so that...
Consider a Poisson distribution in which the offspring distribution is Poisson with mean 1.3. Compute the...
Consider a Poisson distribution in which the offspring
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X is a random variable following Poisson distribution. X1 is an observation (random sample point) of...
X is a random variable following Poisson distribution. X1 is an
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(1.1) Please find probability distribution of X and X1. Make
sure to define related parameter properly.
(1.2) Please give the probability distribution of a random
sample with sample size of n that consists of X1, X2, ..., Xn as
its observations.
(1.3) Please give an approximate distribution of the sample mean
in question 1.2(say, called Y) when sample size is 100 with
detailed...
1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find...
1. If the random variable x has a Poisson Distribution with mean
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Round your answer to two decimal places.
2.
In one town, the number of burglaries in a week has a Poisson
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(HINT:...
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When we reject a null hypothesis, we are certain that the
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True or False
Why do we test the null hypothesis and not our research hypothesis?
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The Poisson probability distribution, associated with a waiting line, is characterized by a parameter known as...
The Poisson probability distribution, associated with a waiting
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Explain this concept and describe its connections with the
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