The autocorrelation function $R_X(\tau)$ of a wide-sense stationary random process $X(t)$ is shown in the figure.

$$ \text { The average power of } X(t) \text { is ___________} $$

The random variable

$$ Y=\int_{-\infty}^{\infty} W(t) \phi(t) d t, \quad \text { where } \phi(t)=\left\{\begin{array}{cc} 1, & 5 \leq t \leq 7 \\ 0, & \text { otherwise } \end{array}\right. $$

and $W(t)$ is a real white Gaussian noise process with two-sided power spectral density $S_W(f)=3 \mathrm{~W} / \mathrm{Hz}$, for all $f$. The variance of $Y$ is $\_\_\_\_$ .

Consider the random process
x(t) = U + Vt.
Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is _________________

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