Questions tagged [probability]

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53 views

linear minimum mean squared error estimate under Gaussian prior

I am learning estimation theory through Steven M.Kay's book Fundamentals Of Statistical Signal Processing--Estimation Theory. In the ...
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2answers
125 views

Power Spectral Density from Probability Density Function

The samples of a signal $x[n]$ are i.i.d. and follow a triangular pdf with $a = 0,\ b = 2,\ c = 1$: The DC-power of the signal is $$\mu_x^2 = \big(\mathbb{E}(X)\big)^2 = \left(\int_{-\infty}^{\infty} ...
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3answers
81 views

Determining Loss of Information by Taking Average (Mean of Signal)

So basically information is defined by expected value of Shannon's information i.e. Entropy. I am curious how much information is lost if we simply take the average of the sample given to us. I am ...
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0answers
39 views

Expectation of a constant diagonal matrix

Is the expected value of a diagonal matrix with constant entries equal to the mean value of the entries? My question stems from the following observation in a paper. Given a real diagonal matrix $\...
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0answers
15 views

About convergence of KL divergence: if the two probability distributions are type, does the law of large number work?

If I pick $N$ samples from $P_X$ and $P_Y$, they are two independent discrete distributions. $X_1,X_2,\ldots,X_N$ are drawn i.i.d from $P_X$, and $Y_1,\ldots,Y_N$ are drawn i.i.d from $P_Y$. I got $...
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1answer
74 views

How to get info (mean,std) out of normplot in matlab?

Lets say we have the following data and then we have a normplot: load census; h=normplot(cdate); [mean std]=normfit(cdate); I know i can get the mean(1890) and ...
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1answer
21 views

Interference Distribution Assumption in NOMA IoT Scenario

I am assuming a NOMA IoT Uplink scenario, which is interference marred. I have to ascertain the SINR at the Access Point (AP) for the NOMA users. A sub-channel is allocated to various users and ...
-1
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2answers
63 views

Probability of error for detection problem

Let $X \in \mathbb{R}^N$ and $Z \sim \mathcal{N}(0, \sigma^2 I)$ be random vectors. $Y = X + Z$ $X$ can be either $a_0 \in \mathbb{R}^N$ or $a_1\in \mathbb{R}^N$ with equal probability. So the ...
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0answers
24 views

Pairwise error probability representation problem

i am looking to make a comparison between theoretical and simulation results for pairwise error probability data. I have a MIMO system using Space-time coding. I am required to produce simulation ...
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0answers
35 views

Information entropy of Poisson noise

I would like to calculate the information entropy of the channel with additive Poisson noise. The model consists of an input signal, an optical image, an image acquisition device, and the output ...
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0answers
33 views

Pairwise Error Probability simulation versus SNR for Space-time code

I have a MIMO system using Space-time coding. I am required to produce simulation results in the form $\text{PEP}=f(\text{SNR})$, meaning a curve representing the Pairwise Error Probability (PEP) for ...
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1answer
46 views

Understanding Asymptotic Equipartition Property

I have some problems in understanding the precise meaning of the Asymptotic Equipartition Property, related to a large number n of independent and identically distributed random variables (X1, X2, ...,...
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3answers
82 views

Why is the median of a PDF not always equal to the mean? [closed]

When studying probability density functions(PDFs), the focus is often placed on the "mean" and not the "median". The mean is often described as the center of mass of the PDF. I've always taken this as ...
3
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1answer
101 views

How to Linearly Combine Two Unbiased Estimators of One Parameter without Knowledge of Their CoVariance?

I have two unbiased estimators of one parameter, $\tau$. The first estimator, $r_1$, is the better estimator with lower variance than the second estimator, $r_2$. I also have: $ \mathbb{E} \left[ {r}...
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2answers
154 views

Understanding the Probability Distribution of Intensity Values

From "Digital Image Processing 4th ed. - Gonzalez, Woods" Let $p_r(r)$ and $p_s(s)$ denote the PDFs of intensity values $r$ and $s$ in two different images. A fundamental result from probability ...
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3answers
9k views

What Do Skewness and Kurtosis Represent?

I understand that the question could mean a lot of things but I am thinking specifically to image processing. For example, I know that the mean can be a basic texture feature that represents the ...