An enhancement MOSFET of threshold voltage 3 V is being used in the sample and hold circuit given below. Assume that the substrate of the MOS device is connected to -10 V . If the input voltage $v_1$ liesbetween $\pm 10 \mathrm{~V}$, the minimum and the maximum value of $v_G$ required for proper sampling and holding respectively, are

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 $\_\_\_\_$ .

A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous of at least one of its bits is decoded wrongly. The probability that the received block is erroneous, is

A binary random variable $X$ takes the value +2 or -2 . The probability $P(X=+2)=\alpha$. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is maximum, is $\_\_\_\_$ .