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| give mean, variance for single random variable. what will happen when variance = 0? |
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Definition
| when variance = 0 this means they are really close to average |
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Definition
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| what's mean for two random variables? |
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Definition
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| give equation for correlation of X and Y |
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Definition
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| give equation for covariance of X and Y |
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Definition
| E[(X-u)(Y-u)] = E[xy] - UxUy |
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| give equation for correlation coefficient of X and Y |
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Definition
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| of correlation coefficient is 0, then what does that mean? |
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Definition
means X and Y are uncorrelated.
p = 0 -> cov(x,y) = 0 -> E[xy] = UxUy |
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| Why is plotting Q helpful? |
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Definition
| usually tail probability is the error |
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Definition
| thi[ (x - mean)/variance square rooted ] |
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| how to find mean and variance of two RV given one RV |
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Definition
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| X and Y are independent in Gaussian RV if? does X and Y uncorrelated means X and Y are independent in general>? |
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Definition
X and Y are not correlated.
X and Y uncorrelated does not mean X and Y are independent, but for Gaussian RV, it is |
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Definition
Event is random given any t. For random variable case, t was = 1 only, but this one is for any t.
evolution of random variables with respect to t |
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| explain why a signal is a random process |
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Definition
1. signals are function of time
2. don't know what waveform will look like unless experimented |
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| what are two types of random process in signals? |
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Definition
1. transmitted signals
2. noises |
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| what is mean of a random process X(t)? does the mean depend on t? |
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Definition
| look at txt book. Yes it depends on t |
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| give an equation for auto-correlation of random process X(t) |
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Definition
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| give an equation for cross-correlation of random process X(t) and Y(t) |
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Definition
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Definition
1. if mean doesn't depend on t
2. if autocorrelation doesn't depend on t |
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| what are 4 properties of autocorrelation of a WSS process? |
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Definition
1. Rx(tao) = Rx(-tao)
2. |Rx(tao)| <= Rx(0) for all tao
3. Rx(tao) <-> Sx(f):psd of X(t) is FT of Rx(tao)
4. Rx(0) = E[X^2] |
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Definition
| average power of a signal |
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| what are 4 properties of LTI system for WSS? |
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Definition
1. if input is WSS, then output is also WSS
2. Uy = UxH(0)
3. Ry(tao) = Rx(tao)*h(tao)*h(-tao)
4. Sy(f) = Sx(f)|H(f)|^2 |
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| what is equation for cross spectral density? |
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Definition
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| What properties does white gaussian noise have? |
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Definition
1. properties of WSS process
2. mean = 0
3. auto-cor = N0/2 delta(t)
4. Gaussian RV
4. PSD = N0/2 |
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| if a process is WSS, then PSD exists? |
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Definition
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| If a WGN passes through LPF, is it still a WGN? |
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Definition
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