- Better Alien Detection Techniques

Although the average heartbeat rate is quite different for humans and RAD2 population (74 beats/min versus 95 beats/min), dispersion of measurement (noise and fluctuations) makes it difficult to achieve a good probability of detection for a given false alarm rate (P_d = 35.5 %, P_fa = 1%).

Further studies show that these fluctuations were more due to physical activity, mood and stress than to physical characteristics and that the heartbeat rate of a specific individual can vary randomly from one measurement to the other with a density function given by table 3 (exercise 2).

To make detection more reliable, it was decided to average four independent measurements for each candidate before comparing to the threshold.

Question

Assuming that the human heartbeat rate also fluctuates randomly for a given individual, what is the P_d achieved with the same P_fa (1%) for RAD2 general population?

Note:

From table 1 (problem 1) we can calculate the mean value and the standard deviation of a human (m₀ = 74.3, s₀ = 9.9) and from table 4 (problem 2) we calculate mean value and standard deviation for a RAD2 individual (m₁ = 95, s₁ = 14)