# Tag Info

Accepted

### Understanding of Random Process, Random Variable and Probability Density Function

when we observe the Random Process at a specific time $t_k$, that is the value at $X(s_1,t_k), X(s_2,t_k),\ldots,X(s_n,t_k)$, if we denote them by $(a_1,a_2,\ldots, a_n)$. Now the mapping between ...
• 6,605
Accepted

• 28.3k
Accepted

### Understanding Asymptotic Equipartition Property

The sentences you've mentioned in your question all have a quite different meaning. Let me try to explain them one by one: Clearly, it is not true that all $2^n$ sequences of length $n$ have the ...
• 90.5k

### If $X$ and $Y$ are zero mean independent Gaussian random variables with different variances, what is the density of $\sqrt{X^2+Y^2}$

According to your description, $x = Z \cdot \cos(W),\ y = Z \cdot \sin(W)$. Follow this answer for the derivation of joint PDF of $(Z, W)$ : Complex Gaussian Magnitude and Phase Joint PDF Derivation ...
• 2,611
Accepted

### How can I generate time-variant Rayleigh channel in MATLAB

Yes, you can have time variant channel in MATLAB either by using comm.RayleighChannel() , you can read about it in help of matlab. or the other way you use the ...
• 1,056
Accepted

### Autocorrelation of random walk

Let's try to figure this out from first principles. Let's start with $x$ our zero-mean, Gaussian, independent, identically distributed noise sequence: $$x[n] \sim N(0,\sigma^2_x)$$ Then our random ...
• 25.9k
1 vote
Accepted

### Determining the average probability of error

Note that $$\mathbb{P}(n_m+i_m<-1\cap i_m = \frac{-1}{2})$$ is equal to $$\mathbb{P}(n_m < -0.5)\mathbb{P}(i_m = -0.5) = 0.25\mathbb{P}(n_m < -0.5)$$ since $n_m$ and $i_m$ are independent....
• 15.3k
1 vote
Accepted

### Why the requirement of the GCD of the lengths of all circuits in the graph being one?

This is my understanding: the statistics of the source described in the paper depend on which character is produced first. If the first character is $a$, then one of the source properties is that ...
• 15.3k
1 vote

### Why is there only one integration in the solution if there is two integral in the formula?

You have the definition of the random process as : $$X(t) = a \sin(\omega_0 t + \Theta) \tag{1}$$ where $a$ and $\omega_0$ are deterministic constants and $\Theta$ is a continuous R.V. uniformly ...
• 28.3k
1 vote

### Why is there only one integration in the solution if there is two integral in the formula?

You have a single random variable $\Theta$ in this example, so taking the expectation with respect to that random variable results in a single integral. The formula for $R_X(\tau)$ in your question is ...
• 90.5k
1 vote
Accepted

• 90.5k
1 vote

### Random Process at a particular time instance

Your equation (3) and (4) are wrong. When you say Also, the sum of probabilities of a random variable should be 1 you actually mean the total sum of the values of probability mass function \$P_{...
• 28.3k
1 vote

### How can I calculate the entropy of a signal that's not independent from itself?

I think that the answer is that there is no correct answer. Whilst this is a simple question, the answer is kinda open. You're asking about the entropy of correlated data with respect to random ...
• 392

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