Monte-Carlo method

Question

I have a problem with my statistics task. It sounds like this: "Using the Monte Carlo method, plot the dependence of a on b for a from -5 to 5, where $P (a < x-y < b) = 0.95$, where $x\sim N(0,1)$, and y is a uniformly distributed random variable from -2 to 2." what should I do, where to start? until I have no ideas.

To be honest, I did not understand anything in the following answer: "First find the probability distribution of random variable X−Y using montecarlo method.

1.Pick an x and y randomly according to their densities and then compute x−y. Do this N times.

2.Make a list x−y values.

3.Sort the list in ascending order.

4.Fix an b which is in [−5,5].

5.From count number of values less than b, call this k.

$\cdot$ If k/N>0.95: Count from smallest value till you get the k/N less more or less equal to 0.95. The value you find is the a

$\cdot$ If k/N<0.95:

No such a exists."

I tried to code it and I have a lot of questions.

First of all, I created a list for $x-y$.

 dif<-x-y

Then, I created a list of values of a, which is from -5 to 5

a<-seq(-5, 5, 0.05)

But now I must go to the 5-th item. It sounds like this: From count number of values more than a, call this k. What should I do here? I must take values from $x-y$, which are more than a? Then I should count $k/N$ and if it is more than 0.95 what is next? "Count from smallest value", but what smallest value?

Thanks for help

Welcome to MSE. Please use MathJax. – José Carlos Santos Dec 20 '17 at 08:46 — José Carlos Santos, Dec 20 '17 at 08:46

score 4 · Answer 1 · answered Dec 20 '17 at 08:53

4

First find the probability distribution of random variable $X-Y$ using montecarlo method.

Pick an $x$ and $y$ randomly according to their densities and then compute $x-y$. Do this $N$ times.
Make a list $x-y$ values.
Sort the list in ascending order.
Fix an b which is in $[-5,5]$.
From count number of values less than $b$, call this $k$.
- If $k/N>0.95$
  - Count from smallest value till you get the $k/N$ less more or less equal to 0.95.
  - The value you find is the $a$
- If k/N<0.95
  - No such a exists.

answered Dec 20 '17 at 08:53

Sonal_sqrt

4,711

Thanks a lot for your help ! – user515149 Dec 20 '17 at 12:07
Were you able to get results? – Sonal_sqrt Dec 20 '17 at 12:10
Not yet, but the idea is clear . but I have a question: why we must fix b from [-5,5]? in the initial statement of the problem a is from -5 to 5 – user515149 Dec 20 '17 at 12:35
So you might be wanting to find $b$ as a function of $a$, can you figure what change it would require in the algorithm? – Sonal_sqrt Dec 20 '17 at 12:43
I must fix a from -5 to 5 and then from count number of values more than a? – user515149 Dec 20 '17 at 12:56
1

You got it, I will add that in an edit – Sonal_sqrt Dec 20 '17 at 12:57
So I began to code this and the problem appeared. Let a is a list of values from -5 to 5. Now I must do 5-th item that is:From count number of values more than a call this k... And the question is: What is the greatest value of k I should choose in the loop? – user515149 Dec 23 '17 at 11:42
1

Just count numbers of $x-y$ values between the $a$ and $b$. – Sonal_sqrt Dec 23 '17 at 11:50
I understood, thank you – user515149 Dec 23 '17 at 12:17
In 6-th item you have:"less more or less equal ", I can't understand what you said – user515149 Dec 23 '17 at 13:54

Monte-Carlo method

1 Answers1