If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be

Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X, Y] is less than 1/2 is

The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X^2}\,(t)} \right]$$ and $$E\,\left[ {X\,(t)} \right]$$, respectively, are

If E denotes expectation, the variance of a random variable X is given by