The voltage received at a radio is modeled as a random variable X. When there is no transmit signal, the voltage is uniformly distributed between -2 and 2 Volts. When there is a transmit signal, the voltage is uniformly distributed between 0 and +3 Volts. Suppose that a signal is transmitted with probability 0.75 (and no signal is transmitted with probability 0.25).

a. Find the pdf of X.

b. Given that the voltage received is X = 1.5 Volts, calculate the probability that a signal was transmitted.