MATLAB: Find intersection of 2 normal distribution

equationfindfsolvefzerointersectionsolve

Hi,
I have 2 normal pdf and I want to find their intersection:
Screen Shot 2019-10-16 at 14.39.05.png
the intersection is between 160 to 170.
I have code as follows:
mu1 = 160;  
var1 = 20;
mu2 = 175;
var2 = 15;
yfun = @(mu,var, x)(2*pi*(var))^(-0.5)* exp(-((x-mu).^2)/(2*(var)));
val = fzero(@(x) yfun(mu1, var1, x) == yfun(mu2, var2, x), rand * (mu1 - mu2) + (mu1 + mu2))
Output:
val =
  324.6802
Its the value of 2nd parameter of fzero() and fzero() sets val to it's 2nd parameter whatever i change it to.
How do i find the intersection's x value?

Best Answer

The ‘val’ value is the x-value of the intersection, however you need to start fzero in the correct region for it to return the correct value. It is then straightforward to calculate the y-value from either Gaussian function, since they are both approximately the same at that point.
I changed your code slightly so it returns the correct results: 
mu1 = 160;  
var1 = 20;
mu2 = 175;
var2 = 15;
yfun = @(mu,var, x)(2*pi*(var))^(-0.5)* exp(-((x-mu).^2)/(2*(var)));
val = fzero(@(x) yfun(mu1, var1, x) - yfun(mu2, var2, x), mean([mu1,mu2]))
yval = yfun(mu1, var1, val)
producing: 
val =
          167.872647061767
yval =
        0.0189439821229373
Experiment to get the result you want.
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