Home › Previous year questions › GATE 2017 EC (EC2) › Question 32GATE 2017 EC (EC2) – Question 32 Communications · Random Processes · 1 mark · Numerical answer
Consider the random process $X(t)=U+Vt$, where U is a zero-mean Gaussian random variable and V is uniform between 0 and 2. Assume U and V are statistically independent. The mean value of the process at t=2 is ________.
Practise this question in The GATE Grind →
Show answer and explanation Correct answer: 2.0 to 2.0
Explanation Linearity of expectation gives $E[X(t)]=E[U]+tE[V]$. The Gaussian variable has mean zero, and the uniform variable has mean $(0+2)/2=1$.
At t=2, $E[X(2)]=0+2(1)=$ **2**. Independence is part of the model, but linearity of expectation alone is sufficient for this mean calculation.
More Random Processes questions GATE 2016 EC (EC2) Q60 – Let X(t)=3V(t)-8, where V is a zero-mean stationary process with autocorrelation R… GATE 2016 EC (EC3) Q59 – A wide-sense stationary process X(t) passes through the shown delay-and-subtract LTI… GATE 2025 EC Q42 – Consider a real-valued random process f(t)= n=1Na n\,p(t-nT), where T>0 and N is a… GATE 2024 EC Q20 – A white Gaussian noise w(t) with zero mean and power spectral density N 02, when applied… GATE 2024 EC Q57 – Let X(t)=A(2 f 0t+) be a random process, where amplitude A and phase are independent of… GATE 2023 EC Q30 – For a real signal, which of the following is/are valid power spectral density/densities? All Random Processes questions →