variance

A white Gaussian noise w(t) with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order RC low pass filter produces an output n(t). At a particular tim...

A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular...

Two continuous random variables X and Y are related as Y = 2X + 3. Let $$\sigma _x^2$$ and $$\sigma _y^2$$ denote the variances of X and Y, respectively. The variances are related...

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{arra...

The second moment of a Poisson-distributed random variables is $$2.$$ The mean of the random variable is _______.

The variance of the random variable $$X$$ with probability density function $$\,f\left( x \right) = {1 \over 2}\left| x \right|{e^{ - \left| x \right|}}\,\,$$ is ___________.

Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mean values of $$X$$ and $${{X^2}}$$, respectively. The relatio...

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

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

If the variance $$\sigma _d^2$$ of d(n) = x(n - 1) is one-tenth the variance $$\sigma _x^2$$ of a stationary zero-mean discrete-time signal x(n), then the normalized autocorrelatio...

The variance of a random variable X is $$\sigma _x^2\,.$$ Then the variance of - kx (where k is a positive constant ) is