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统计代写|ST308 Bayesian Analysis

MY-ASSIGNMENTEXPERT™可以为您提供lse.ac.uk ST308 Bayesian Analysis贝叶斯分析课程的代写代考辅导服务!

这是伦敦政经学校贝叶斯分析课程的代写成功案例。

数学代写|STAT6570 Bayesian Analysis

ST308课程简介

This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

Teaching

This course will be delivered through a combination of classes, lectures, and Q&A sessions, totalling a minimum of 29 hours across the Lent Term. This course does not include a reading week and will be concluded by the end of week 10 of Lent Term.

Prerequisites 

Students must have completed one of the following two combinations of courses: (a) ST102 and MA100, or (b) MA107 and ST109 and EC1C1. Equivalent combinations may be accepted at the lecturer’s discretion. ST202 is also recommended.

Previous programming experience is not required but students who have no previous experience in R must complete an online pre-sessional R course from the Digital Skills Lab before the start of the course (https://moodle.lse.ac.uk/course/view.php?id=7745)

ST308 Bayesian Analysis HELP(EXAM HELP, ONLINE TUTOR)

问题 1.

In an experiment on extra-sensory perception (ESP) a person, A, sits in a sealed room and points at one of four cards, each of which shows a different picture. In another sealed room a second person, B, attempts to select, from an identical set of four cards, the card at which A is pointing. This experiment is repeated ten times and the correct card is selected four times.
Suppose that we consider three possible states of nature, as follows.
State 1 : There is no ESP and, whichever card A chooses, B is equally likely to select any one of the four cards. That is, subject B has a probability of 0.25 of selecting the correct card.
Before the experiment we give this state a probability of 0.7 .
State 2 : Subject B has a probability of 0.50 of selecting the correct card.
Before the experiment we give this state a probability of 0.2 .
State 3 : Subject B has a probability of 0.75 of selecting the correct card.
Before the experiment we give this state a probability of 0.1 .
Assume that, given the true state of nature, the ten trials can be considered to be independent.
Find our probabilities after the experiment for the three possible states of nature.
Can you think of a reason, apart from ESP, why the probability of selecting the correct card might be greater than 0.25 ?

问题 2.

In a certain small town there are $n$ taxis which are clearly numbered $1,2, \ldots, n$. Before we visit the town we do not know the value of $n$ but our probabilities for the possible values of $n$ are as follows.
\begin{tabular}{|cccccc|}
\hline$n$ & 0 & 1 & 2 & 3 & 4 \
Probability & 0.00 & 0.11 & 0.12 & 0.13 & 0.14 \
\hline$n$ & 5 & 6 & 7 & 8 & $\geq 9$ \
Probability & 0.14 & 0.13 & 0.12 & 0.11 & 0.00 \
\hline
\end{tabular}
On a visit to the town we take a taxi which we assume would be equally likely to be any of taxis $1,2, \ldots, n$. It is taxi number 5 . Find our new probabilities for the value of $n$.

问题 3.

In a forest area of Northern Europe there may be wild lynx. At a particular time the number $X$ of lynx can be between 0 and 5 with
$$
\operatorname{Pr}(X=x)=\left(\begin{array}{c}
5 \
x
\end{array}\right) 0.6^x 0.4^{5-x} \quad(x=0, \ldots, 5) .
$$
A survey is made but the lynx is difficult to spot and, given that the number present is $x$, the number $Y$ observed has a probability distribution with
$$
\operatorname{Pr}(Y=y \mid X=x)=\left{\begin{array}{ll}
\left(\begin{array}{l}
x \
y
\end{array}\right) 0.3^y 0.7^{x-y} & (0 \leq y \leq x) \
0 & (x<y)
\end{array} .\right.
$$
Find the conditional probability distribution of $X$ given that $Y=2$. (That is, find $\operatorname{Pr}(X=0 \mid Y=2), \ldots, \operatorname{Pr}(X=5 \mid Y=2)$ ).

问题 4.

A particular species of fish makes an annual migration up a river. On a particular day there is a probability of 0.4 that the migration will start. If it does then an observer will have to wait $T$ minutes before seeing a fish, where $T$ has an exponential distribution with mean 20 (i.e. an exponential(0.05) distribution). If the migration has not started then no fish will be seen.
(a) Find the conditional probability that the migration has not started given that no fish has been seen after one hour.
(b) How long does the observer have to wait without seeing a fish to be $90 \%$ sure that the migration has not started?

数学代写|ST308 Bayesian Analysis

MY-ASSIGNMENTEXPERT™可以为您提供LSE.AC.UK ST308 BAYESIAN ANALYSIS贝叶斯分析课程的代写代考和辅导服务!

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