# Items tagged with probabilityprobability Tagged Items Feed

### Walk in random direction...

December 03 2015
2 3

Hei, I'm trying to create a random walk in the plane, with constant step length (=1) and the angle between two consecutive steps are decided by a probability density function. I just can't seem to find out how I should implement the density function into my worksheet.

The probability density function is: p(phi)=(1/4)*cos(phi/2), on the interval [-Pi,Pi].
And  I think i managed to do it by selecting a random angle, but don't know how to generate a random angle given this probability function. Any ideas? It'd be highly appreciated!

### Probability density normalization...

November 16 2015
2 2

Probability_density_normalization.mw

In this code I'm trying to separately normalize two independent probability densities and then combine them to get the joint probability density that's normalized and then use it to calculate the probability that the two variables are equal. fD(x) is a Gaussian divided by x^2 and fA(x) is a Gaussian. The first problem occurs when I'm checking the normalization of the joint probability density by doing the double integral over all space for fD(x)*fA(y)dxdy, I get weird vanishing number when the parameter "hartree" takes a certain value, namely 27.211. If I change hartree to 27 or 1 or 2 it all worked, but 27.211 is not good. Also later when I do a single integral over all space for fD(x)*fA(x)dx to get the probability that these two are equal, I find the result is dependent on hartree. This hartree thing is a unit conversion in my physical problem and in principle should not interfere with either the normalization or the probability result at all. I suspect this is a coding bug but I can't find what it is. I'd appreciate any input.

Thank you very much!

Edit: I found out that the problem with the double integral normalization may have something to do with the discretization for numerical evaluation of the integral, since if I change the lower bound to 1/hartree and upper to 10/hartree then it's fine, however if I use lower bound at 1/hartree and upper at 5/hartree it doesn't work, although the distribution has no value between 5/hartree and 10/hartree. However after this is fixed I still have the problem with the single integral over all space for fD(x)*fA(x)dx changing with hartree. Well as a probability I would expect the integral to be bound between 0 and 1, but since it almost linearly depends on hartree, at hartree around 27 I would get the integral value to be about 25, which doesn't make sense. In fact, I now suspect it is not Maple, but my calculation of the probability of the two random variables taking the same value is wrong, I'd appreciate it very much if someone can confirm this.

### Probability of a situation occurance ...

October 17 2015
0 3

I'm drawing a complete blank on this.

The probability of a branch breaking in a particular tree as someone climbs is 2%.  After the person has climbed over 40 branches, did any of them break?  I'm trying to set that up as a simulation in Maple but I'm not sure about how to do it.

I guess if I generate a random number and it falls under .02 it breaks, is that how I determine that?

randomize():

n := 0;
for i to 40 do
ran := evalf(rand()*10^(-12));
if ran < 0.2e-1 then n := n+1: end if:
end do:
print("Branch broke", n, "times")

I'm not sure I've got the probability right.

### Generating sampling points with a known distribut...

July 04 2015
0 5

Hi,

Suppose I have a probability distribution function f(x). I would like to generate points in a

(1) given interval, can be up to infinity

(2) number of points

(3) satisfy the known probability distribution function f(x)

(4) possible other specifications

Is there any build-in option in maple I could use? Or I have to write something manually?

Thank you very much!

### A matter of notation...

June 13 2015
0 7

Dear Maple users

I am unsure how to handle events and their probabilities in Maple. Let's say I know that an event A has the probability say 0.3 and another event B has probability 0.8. I would like to make the following assignments:

P(A):=0.3:

P(B):=0.8

and maybe defining the conditional probability:

P(A|B):=0.55

but I am not allowed to do so in Maple because if will regarded as a function definition. My purpose is to make simple calculations with those probabilities for example:

P(C):=P(A)*P(B)  etc.

My problem is therefore more of a notational problem than a mathematical one. I hope someone can advice me on a proper setup. I am using 2D math notation, by the way. I could of course name the variables containing the probability using simple names like X1, X2, etc., but then I need constantly to remember what they really mean. The above assignments would be much better, because they are easier to handle mentally.

Regards,Erik

### compute the cdf of a piecewise probability distrib...

April 01 2015
1 1

This should be trivial but I am not able to figure out the right syntax to execute it

The pdf is given by :

f_X(x)={ 1/25 *x, 0<=x<5

2/5 -x/25, 5<=x<10

0, otherwise

I have tried to use the "CumulativeDistributiveFunction" so far

### Expected Value of a function...

January 08 2015
0 2

Hello people in Mapleprimes,

I want to do calculations about an expected value.

For example,

expectedvalueofc.pdf

that is, \int_a^b c d \Omega

where, \Omega is a distribution function of c.

But, I don't know whether this equation can be put into worksheet.

Is there no way other than writing this as

\int_a^b c g(c) dc,

where g shows a probability density function.

Can I use Statistics[ExpectedValue] to calculate expected value with a general distribution function, not specified

to normal distribution?

I hope you will give me some hints.

Best wishes.

### conditional probability DICE...

October 29 2014
0 1

What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?

### cross correlation of log-normal pdfs...

June 03 2014
0 8

Please I want to know how to solve this integration.

int(exp(-(ln(y)-2*sigma^2)^2/(8*sigma^2))/(y*sqrt(8*Pi*sigma^2))*exp(-(ln(y+z)-2*sigma^2)^2/(8*sigma^2))/((y+z)*sqrt(8*Pi*sigma^2)), y = 0 .. infinity)

### Monty Hall Problem with 3 and 4 doors...

December 10 2013
1 17

How  can you create a loop for Monty Hall Problem when you have 3 door (1 opening) and then 4 Doors (with 2 openings and possible 2 switches)

### Help with Biased Coin Toss...

November 11 2013
1 2

Hi,

I need help formulating a biased coin toss.

I want to toss a coin 0 being heads and 1 being tails with probabilty 0.495 of getting heads, how do I show whether heads or tails wins??

Thanks

### Probability distribution function...

November 07 2013
1 10

Hello,

would you please help me how can i introduce a probability distribution function to maple in document mode?

I want to calculate integral of x f(x)dx, while I want maple to know f(x) is a probability distribution function.

I do not have any assumption about f(x)(for example normal or exponential distriburion)

Thanks

### Probability [mean, variance of min of a pair]...

September 13 2013
0 3

In a pocket, we have $5$ balls number from $1$ to

### Distance between random points...

September 10 2013
0 0

Let X be the random variable uniformly distributed in the disk centered at the origin O(0,0) with radius 1 and let Y be the random variable uniformly distributed in the square having its vertices A(6,-1), B(9,-2), C(8,-5), and E(5,-4). What is the PDF of the distance between X and Y? Is it possible to find that with Maple? The similar question in three dimensions, replacing a square by a cube and a disk by a solid sphere.

### Student-T Inverse...

June 02 2013
1 3

I need to integrate the Student-T function which is a function of two variables (nu and t). Maple allows me to use this function through this command:

with(Statistics);

PDF(RandomVariable(StudentT(nu)),t);

The integration of this function gives me the probability (p) of certain event (nu is already known):

p=Int(Student,t=-infinity..X)

If I provide the value of X I can compute the integral easily, now the problem appears when I want to...

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