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Math Help - Help me to make equation of three variables

  1. #1
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    Question Help me to make equation of three variables

    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.
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  2. #2
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    Making equation for third variable

    Quote Originally Posted by satwindercse View Post
    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.
    One simple formula that might be used is: z = x + y - x y = x + (1 - x) y

    If 0 < x < 1 and 0 < y < 1
    then (1 - x) y < (1 - x)
    amd
    x + (1 - x) y < x + (1 - x)
    x + (1 - x) y < 1
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  3. #3
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    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?
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  4. #4
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    Question Help me to make equation of three variables

    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?
    Last edited by satwindercse; July 26th 2010 at 08:53 AM.
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  5. #5
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    Quote Originally Posted by satwindercse View Post
    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.
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  6. #6
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    Quote Originally Posted by satwindercse View Post
    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?
    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
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  7. #7
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    Question Help me to make equation of three variables

    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?
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  8. #8
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    How about z=\frac{x+y}{2}?
    when x=0=y, z=0
    when x=1=y, z=1
    and when 0<x<1 and 0<y<1 then 0<z<1.
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