Mean_max

mu1 = 0.5 (slider from -5 to 20, step 0.5)
sig1 = 0.65 (slider from 0.1 to 2, step 0.05)
cdf_{1} = Normal(mu1, sig1, x, true)
mu2 = 1.5 (slider from -5 to 20, step 0.5)
sig2 = 0.2 (slider from 0.1 to 2, step 0.05)
cdf_{2} = Normal(mu2, sig2, x, true)
cdf_{max}(x) = (cdf_{1}(x) * cdf_{2}(x))
cdf_{min}(x) = 1 - ((1 - cdf_{1}(x)) * (1 - cdf_{2}(x)))
true_{max} = Derivative(cdf_{max}(x))
true_{min} = Derivative(cdf_{min})
spdf = Normal(0, sqrt(1), x, false)
scdf = Normal(0, sqrt(1), x, true)
corr = 0 (slider from 0 to 1, step 0.1)
sig_{m}: sqrt(sig1^(2) + sig2^(2) - (((2 * corr) * sig1) * sig2))
alpha: (mu1 - mu2) / sig_{m}
mu_{max}: (mu1 * scdf(alpha)) + (mu2 * scdf((-alpha))) + (spdf(alpha) * sig_{m})
sig_{max}: ((mu1^(2) + sig1^(2)) * scdf(alpha)) + ((mu2^(2) + sig2^(2)) * scdf((-alpha))) + (((mu1 + mu2) * sig_{m}) * spdf(alpha)) - mu_{max}^(2)
pdf_{1} = Normal(mu1, sig1, x, false)
pdf_{2} = Normal(mu2, sig2, x, false)
approx_{max} = Normal(mu_{max}, sqrt(sig_{max}), x, false)
mu_{min}: (mu1 * scdf((-alpha))) + (mu2 * scdf(alpha)) - (spdf((-alpha)) * sig_{m})
sig_{min}: ((mu1^(2) + sig1^(2)) * scdf((-alpha))) + ((mu2^(2) + sig2^(2)) * scdf(alpha)) - (((mu1 + mu2) * sig_{m}) * spdf(alpha)) - mu_{min}^(2)
approx_{min} = Normal(mu_{min}, sqrt(sig_{min}), x, false)
error_{max}(x) = true_{max}(x) - approx_{max}(x)
error_{min}(x) = true_{min}(x) - approx_{min}(x)