GATE EC 2020 Question Paper (02-Feb-2020) (Shift 2)

A transmission line of length 3λ/4 and having a characteristic impedance of 50 Ω is terminated with a load of 400 Ω. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is ______ Ω

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

The loop transfer function of a negative feedback system is

$G\left(s\right)H\left(s\right)=\frac{K\left(s+11\right)}{s\left(s+2\right)\left(s+8\right)}$

The value of K, for which the system is marginally stable, is

The random variable

$Y=\underset{-\infty }{\overset{\infty }{\int }}W\left(t\right)\varphi \left(t\right)dt,$ where

≤ft( t )= ≤ft\{ {*20c 1;&5 ≤ t ≤ 7\\ 0;&Otherwise } \}

And W(t) is a real white Gaussian noise process with two-sided power spectral density S${}_W$ (f) = 3 W/Hz, for all f. The variance of Y is:

The two sides of a fair coin are labeled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min (M, N), the expected value E(X) (rounded off to two decimal places) is _______