One guy is using the TOGG-1 car with probability 0.6 and the TOGG-2 car with probability 0.4 on his way to LA. The speed it makes with TOGG-1 has a uniform pdf between 70 and 170. With TOGG-2, its speed is between 100 and 200 uniform pdf.

a) One day this guy goes to LA, but we do not know which model he bought. Find and draw the pdf of its speed.

b) Find the mean and variance of the velocity on this journey by taking the total average theorem, that is, consecutive averages.

c) Since the police radar detects that the speed is above 120, find the conditional pdf of the speed. In this case, calculate the probability that the model used is TOGG-1.