hexsol

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These are questions asked by hexsol

Hi

I was wondering how one uses maple to solve for variables that comprise the limits of an integral?

X and R are between 0 and 1.

Any thoughts would be greatly appreciated, thanks in advance...!

Download Solvingforlimitsofintegrals.mw

Hi

I found the Manipulate Equation command tool in Maple and was wondering whether it could help me rearrange my equations into giving me certain quotient? One can do it by hand, but at an exam, time saved makes a difference and one can make silly mistakes. The math rearangement is also rather trivial...

Download rearrangemanipulate.mw

Any thoughts would be greatly appreciated, thanks in advance..!

Hi

I am trying to evaluate the following, and have tried the following commands;

How do I evaluate such an expression, is there a way to get around the invalid product error in the "coded approach"? Obviously the latter doesn't work, Maple naturally needs information concerning the limits, how does one apply assumptions to this more "traditional notation"?

Any thoughts would be greatly appreaciated, thankyou in advance.

Download integratederivative.mw

Hi

I am trying to follow a textbook example concerning the calculations of probability based on continous joint distributions. I cannot calculate the same result using Maple, specifically the double integral.

In a effort to determine what I need help with I have presented the example and what I know, in order to potentially rule out potential misconceptions with regard to the theory itself and maybe not a lack of Maple skills..

The example is a follows;

 

My thoughts / attempt:

So we are dealing with independent variables which are exponetially distributed. We need to find the prob. that P(X<Y), so we need to find the joint density of the distributions. We know the density of an exponential distributed variable, and since they are independent, the product of their densities is the desired joint density function f(x,y) we need in order to evaluate the probabilty;

f(x, y) = lambda*exp(-lambda*x)*mu*exp(-mu*x)

My book states that the probability of a set B, w.r.t to two continuous distributions is

so with regard to my specific case, B can be substituted with X<Y, and as such should also be applied appropriately to the limits of the integrals.

We know that both distributions have the same exponential distribution (in) [0,+inf], and that X<Y is to be determined, thus we can conlude that

{(x,y) : 0 < x < y < +inf}

Thus the probability is given by (as presented in the book):

Can Maple directly solve this integral from such an expression?

The book chooses to split up the double integral with respect to the limits of the variables(distributions?);

x is of course the lowerbound for the dy integral as y is specfied to be larger than x..

So ultimately my problem is that I cannot replicate the last integral expression ,I end up with;

-lambda*exp(-lambda*x - mu*y) + lambda*exp(-lambda*x - mu*x)

So an additional term.. I am just ignorant, and should I ultimately know that I have to disregard the contribution term containg the y variable seeing that we have to inetgrate w.r.t to the last dx integral?doubleintegralprobability.mw

``

``

int(lambda*mu*exp(-lambda*x-mu*y), y = x .. infinity)

limit(-lambda*exp(-lambda*x-mu*y)+lambda*exp(-lambda*x-mu*x), y = infinity)

(1)

``

``

``

``

``

``

NULL

`assuming`([simplify(combine(int(lambda*mu*exp(-lambda*x-mu*y), y = x .. infinity)), size)], [x > 0, y >= x, y > 0])

limit(lambda*(-exp(-lambda*x-mu*y)+exp(-x*(lambda+mu))), y = infinity)

(2)

NULL

NULL

NULL

NULL

NULL

NULL

NULL

int(lambda*mu*exp(-lambda*x-mu*y), y = x .. infinity)

limit(-lambda*exp(-lambda*x-mu*y)+lambda*exp(-lambda*x-mu*x), y = infinity)

(3)

``

Download doubleintegralprobability.mw

Any thoughts would be greatly appreciated, thanks in advance.

 

Hi Mapleprimes,

I am having difficulties trying to evaluate the following integral

int(-(C__A*K + 1)/(k*C__A), C__A = C__A0 .. C__A)

int(-(C__A*K + 1)/(k*C__A), C__A = C__A .. C__A0, numeric = false)

Where the limits are undefined(unknown) symbolic limits, C_A0 is intial concentration, CA is actual concentration. Maple returns the same equation when I try it. I haven't loaded any packages.

I could of course just evaluate the indefinite version and manually substitute but I think that defeats the purpose of using maple.

Any thoughts will be greatly appreciated.

Maple 2020.1

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