A person will be classified as high (class 1) or low risk (class2) of heart diseases using a single measurement and the maximum a posteriori decision rule.

• Assume the conditional probability densities are Gaussians with mean 7 for class 1 and  8 for class 2. The variance is equal to one for the two classes.
• Class 1 and class 2 are equally probable.

• Provide the decision rule for this problem
• Include all mathematical procedures

Hints:

P(x∣C1)=1√2πσexp(−12)P(x∣C1)=12πσexp⁡(−12) P \left(x\mid C_{1}\right) = \frac{1}{\sqrt{2\pi \sigma}} \exp{\left(-\frac{1}{2}\right)}