Every 5 minutes a satellite sends an almost instantaneous signal burst to a ground station to communicate that all systems are working properly. The satellite will not transmit the burst if there is an error somewhere. The transmitted signal strength is 4 units. The signal received at the ground station is a combination of the transmitted signal burst plus or minus noise.
Assume the noise is a normally distributed random variable with mean 0 and variance 2. A design problem is to set the threshold for declaring a signal burst was received, thereby declaring all systems are working properly on the satellite.
Assume the satellite system status is a random variable with probability of 0.7 that all systems are working properly and 0.3 that something is wrong.
a) Simulate the received signal at the ground station for 24 hours.
b) Because of equipment constraints, the receive signal threshold may be set at 2, 3, or 4. Analyze the system for these thresholds and justify a recommendation for setting the threshold level.
MATLAB is preferred for simulation but Excel is also ok. Please show all work. Thank you.