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Results tagged with self-study
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user 109101
A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.
1
vote
1
answer
482
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Conditional probability of an event given a cumulative probability
The outcome of a random variable X is
$X = \{0, 1, 2, 3, 4\}$
with associated probabilities
$P\left(X\right)=\{0.6, 0.2, 0.1, 0.05, 0.05\}$
I would like to compute
$P\left(x=0|x \leq3 \r …
- 251
1
vote
0
answers
30
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Bayes rule and conditional - marginal factorisation (joint posterior)
I have some confusion regarding Bayes rule for joint posterior (I think primarily due to the context in which notations are used)
Let $P(\theta_{1}, \theta_{2} | X)$ be a joint posterior over the para …
- 251
0
votes
0
answers
52
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Determining minimum probability for a standardised variable using the Chebyshev inequality [duplicate]
A report on rural water resources states that the nitrate level of wells in a certain groundwater system has a probability distribution
whose mean and standard deviation are 5.2, 2.1 ppm, respect …
- 251
0
votes
1
answer
68
views
conditional expectation substitution in Fisher information [duplicate]
The Fisher information is given by
$$J(\theta) = -E\left[\frac{d^{2}\log p(x | \theta)}{d\theta^{2}} \bigg|~\theta\right]$$
To consider the Fisher information for a binomial parameter:
Let $p(x | \the …
- 251
0
votes
1
answer
46
views
Understanding physical significant of conditional probability in this event
Question: The probability that a randomly chosen record has an error is 0.05. An error in a record is either large or small. Two out of ten errors, on average, are large.
a. What is the probabili …
- 251
0
votes
1
answer
46
views
Probability that event one and event occurring simultaneously
The sample space for different ratings of food is given in the table below:
For the rating by two person, what is the probability that one of the two will rate the meal as excellent and the other w …
- 251
1
vote
2
answers
239
views
probability of a function of poisson random variable
Please refer to an excerpt from a text titled Essentials of Stochastic Process by Durret.
Here comes a Lemma, built on the above argument.
Lemma: $N\left ( s \right )$ has a poisson distributi …
- 251
0
votes
1
answer
80
views
Metropolis - Hastings sampling: histogram shapes looks sane but bin values are off
The target distribution is of the form:
$ p(x) = x^{-6}.e^{\frac{-2.475}{x}}$ with a support in the interval $[0.0, 2.0]$.
This gives a plot like
Now, to choose a proposal kernel, I think a lognormal …
- 251