# How to evaluate this probability

• GW008
In summary: I think now you might get what I am want to tell...In summary, the probability of an event, defined by the set: {(x,y,z) such that z + x*y/(y+a) > x/(x*k+1)} is not always 1. For any positive value of k, P become higher than one which is unacceptable.

#### GW008

P={ z + x*y/(y+a) > x/(x*k+1)}
where x,y,z are exponentially distributed with mean xbar,ybar,zbar.
a,k are constants.
please suggest me how to evaluate this probability...
for k=0, P lies between 0 and 1 but for any positive value of k, P become higher than one which is unacceptable...
take xbar=1 ybar=3.14 zbar=1

GW008 said:
P={ z + x*y/(y+a) > x/(x*k+1)}
where x,y,z are exponentially distributed with mean xbar,ybar,zbar.
a,k are constants.

Your notation is unclear. Are you asking for the probability P of an event defined by the set:
{(x,y,z) such that z + x*y/(y+a) > x/(x*k + 1) } ?

for any positive value of k, P become higher than one which is unacceptable...
take xbar=1 ybar=3.14 zbar=1

How did you arrive at that conclusion?

Stephen Tashi said:
Your notation is unclear. Are you asking for the probability P of an event defined by the set:
{(x,y,z) such that z + x*y/(y+a) > x/(x*k + 1) } ?

sorry for applying equal to sign, Yes u asking me right question

How did you arrive at that conclusion?

I try to solve this probability but I didn't get its close form so I plot it in MATLAB for different values of xbar.
But as I take the value of k greater than zero, Probability became larger than one...

GW008 said:
so I plot it in MATLAB for different values of xbar.

"It"? Plot what? You aren't stating the problem clearly. What function did you plot?

Stephen Tashi said:
"It"? Plot what? You aren't stating the problem clearly. What function did you plot?

"It refers to probability here.

probability of positive secrecy = P{ z + x*y/(y+a) > x/(x*k+1)}
where x,y,z are exponentially distributed with mean xbar,ybar,zbar.
a,k are constants.
please suggest me how to evaluate this probability...
for k=0, P lies between 0 and 1 but for any positive value of k, P become higher than one which is unacceptable...
ybar=3.14 zbar=1

I tried to solve this Probability to some extent but unable to express Probability in closed form. So, I plot this probability for different values of xbar(0-100). for k=0, this probability decrease from 1 to 0 but for k>0 this probability increase from 1 to 2.5 which is unacceptable...

I think now you might get what I am want to tell...

GW008 said:
"It refers to probability here.

If you are going to plot a function, "it" must be a function. What function are you plotting? What is its formula?

The general form of your question appears to be:

X,Y,Z are independent random variables
f(x,y,z), g(x,y,z) are given functions.
S is the event {(x,y,z) such that f(X,Y,Z) > g(X,Y,Z) }
Find P(S)

But what are you plotting? It wouldn't make sense to plot f(X,Y,Z) or g(X,Y,Z).

If you don't know the formula for P(S), how can you plot anything? You could run a Monte-Carlo simulation and estimate P(S), but that would never produce a number greater than 1.

As event S has three random variables (all are independent) that means P(S) is a case of triple integration. I solve one integration but unable to evaluate other two integrations. In matlab, we can directly plot integral equation using function "integral , integral2, integral3". I use "integral2' to evaluate P(S) and plot it by varying xbar for different values of k...for k=0, this probability decrease from 1 to 0 but for k>0 this probability increase from 1 to 2.5.

It can be happened that i evaluate that first integration wrong or i did some other mistake... Please evaluate P(s)...
Thanks

## What is probability and how is it evaluated?

Probability is the measure of the likelihood of an event occurring. It is evaluated by dividing the number of favorable outcomes by the total number of possible outcomes.

## What is the difference between theoretical probability and experimental probability?

Theoretical probability is based on mathematical calculations and predicts the likelihood of an event occurring. Experimental probability is based on actual observations and experiments, and may differ from theoretical probability due to chance or other factors.

## How do you determine the sample space in probability?

The sample space is the set of all possible outcomes in a given situation. It can be determined by listing all the possible outcomes or by using a tree diagram or table to organize the outcomes.

## What is the difference between independent and dependent events?

Independent events are events in which the outcome of one event does not affect the outcome of another event. Dependent events are events in which the outcome of one event does affect the outcome of another event.

## How do you use probability to make predictions?

To make predictions using probability, you can use the probability of an event occurring to estimate the likelihood of that event happening in the future. You can also use probability to compare the likelihood of different outcomes and make informed decisions.