Matlab problem 1 Solution

Description

You know (Maxwell’s devil told you) that the value of bilirubin in the blood of a healthy person is a Gaussian random variable with mean ₀ and variance ₀²; a person with pancreas tumor has the value of bilirubin in the blood which is again Gaussian with mean ₁ and variance ₁². You decide that the bilirubin test is positive if the measured bilirubin value is above threshold

• .

Write the formulas of your test speci city and sensitivity. Let us say that the incidence of pancreas tumor in the population is p. Write the formulas for the probabilities P (D_yjT_p) that a person really is a ected by pancreas tumor given that the test is positive and P (D_njT_n) that a person really is healthy given that the test is negative.

Write a Matlab script that plots:

1. test sensitivity and speci city as functions of the threshold T

2. P (D_yjT_p) as function of T and p (a surface, you can use mesh or meshc)

3. P (D_njT_n) as function of T and p (a surface, you can use mesh or meshc)

4. the superimposed contour plots of P (D_yjT_p) and P (D_njT_n) at probability values 0:5; 0:9; 0:99; 0:999; 0:9999

Use initially

₀=10, ₀²=4 ₁=15, ₁²=8

then, once you can plot the results for this case, change these values and comment the results.