Let the signalXbe a uniform random variable in the interval 3 - 3, 34, and suppose that a sample of size 50 is obtained.

(a)Estimate the probability that the sample mean is outside the interval 3 - 0.5, 0.54.

(b)Estimate the probability that the maximum of the sample is less than 2.5.

(c)Estimate the probability that the sample mean of the squares of the samples is greater than 3.

(d)Generate 100 random samples of size 50. Compare the probabilities obtained in parts a, b, and c to the observed relative frequencies.