A random voltage X is input to a full wave rectifier that pr

A random voltage X is input to a full wave rectifier that produces at its output the absolute value of the voltage. If X is a standard normal random variable, what is the probability that the output of the rectifier will exceed 2?

Solution

For output to be greater than 2, X is either greater than 2 or les than -2 (As the output is the absolute value of X).

As X is a standard normal variable, we get the probability of X>2 from the standard normal distribution table

Therefore, p=0.02275

As the standard normal distribution is symmetric in nature, p(X<-2)=p(X>2)=0.02275

Therefore, required probability = 2p = 2*0.02275 = 0.0455