I would like to make equation with three (x,y,z) variables to calculate the third variable from two. There is a direct relationship of third variables with other two. For example
Z= aX + bY. i want z should lie between 0 and 1. x and y both are liying between 0 and 1. One method is Pythagoras theorem or distance formula. Can any one help me to form the equation with any other formula? I am in dark kindly help me.
Thanks for ur help.
Can u please tell me the name of the equation known to be? why we subtract the xy from equation.
Other thing is 0 and 1 both are included in x and y. z value is also between 0 and 1 and both 0 and 1 are included in the z in optimal condition?
Can u please help me to project this equation graphically or geometrically?
Thanks for ur help.
Can u please tell me the name of this equation? why we subtract the xy from equation.
Z value is lie between 0 and 1 and both 0 and 1 are included in the Z in optimal condition only? Another thing i want is Z sholud be 0 when x and y both are 0 and Z should be 1 when x and y both are 1 not other than that.
Can u please help me to project or prove this equation graphically or geometrically?
First, equations don't generally have names.
The "xy" was subtracted specifically so that z would be 1 when x and y are both 1: Just x+ y alone would be equal to 2 when x= y= 1 but 1+ 1- (1)(1)= 1.
I don't know what you mean by "optimal condition". There was no mention of "optimal" in your original post.
The formula Kermit1941 gave does exactly what you ask: it is 0 when x and y are 0, 1 when x and y are 1 and only at those points.
I don't know what you mean by "prove" an equation. What do you want to prove about it? -If you mean "prove it is 0 only if x= y= 0", graph y= x/(1- x). If you mean "prove it is 1 only if x= y= 1", graph y= (1-x)/(1- x). If you mean "prove that the equation MUST be this", you can't. There are an infinite number of equations satisfying those conditions Kermit1941 gave you the simplest.
Name of equation: probability that either event A or event B will happen
if probability of event A is x, and probability of event B is y.
The equation remains valid for 0 and 1 values of x and y.
z = x + y - x y
If x is 1, then regardless of the value of y, z is equal to 1.
If x is 0, then regardless of the value of y, z is equal to y.
The subtracting of x y is to insure that
z will be in the range (0 to 1) provided both x and y are in that range.
When both x and y are equal to 1,
z = 1 + 1 - 1 * 1.
Without the subtraction of x y, z would have been 2.
Another way to look at the reason for subtracting x y is this:
x is a measure of something that I give the name of A.
y is a measure of something that I give the name of B.
I want z to be the measure of everything that is in
either A or B.
It is not enough to simply add x and y because
there may be things that are in both A and B.
x y is the measure of those things in both A and B.
So
z = x + y - x y
z = measure of A + measure of B - measure of things in both A and B.
Thus z is the measure of everything that is in A or B. And we count those
things that are in both A and B only once,
instead of twice, by subtracting xy.
Kermit Rose
This equation works satisfactorily for me for all the condition except the following:
when x=1 and y=between 0 and 1 or vice versa.
For Example
when x=1 and y=0.2
then z=1+.2-.2=1
but this is not as per my requirement. I want that z=0 or z=1 should come only when x=y=0 and x=y=1 respectively. Otherwise some value should come.
For me optimal condition are when x=y=1 i.e. (1,1) at this point i want z=1.
Can we do some thing by normalizing this equation?
One of u have talk about some other equation can u please suggest me those?