Exam 6: Modeling Random Data and Noise

The standardized Gaussian PRNG produces Gi and the PRNG value $Y _ { i }$ is uniformly distributed over [0,1).If $\mathrm { G } _ { i } \text { and } Y _ { i }$ are independent, what is the mean and variance of $Z _ { i } = 2 G _ { i } + 4 Y _ { i } - 1$

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Question 1

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$2 \mathrm { G } _ { i }$ has mean 0 and variance $\text { 4. } 4 \mathrm { Y } _ { i }$ has mean 4(0.5)=2 and variance $16 ^ { * } ( 1 / 12 ) = 4 / 3 \text {. Adding } - 1$ gives $\mu _ { z } = 1 \text { and } \sigma _ { z } ^ { 2 } = 4 + 4 / 3 = 16 / 3$

The RV Z is uniformly distributed between -0.15 and 0.35 .What is the amplitude of PDF $p _ { z } ( x )$ that makes the area under the curve equal to 1.

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Question 2

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$\text { Extent } = 0.5 - > p _ { z } ( x ) = 2 \text { for } - 0.15 \leq x < 0.35$

The standardized Gaussian PRNG produces Gi .What is the mean and variance of $Z _ { i } = 2 G _ { i } + 3$

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Question 3

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$2 G _ { i }$ has mean 0 and variance 4.Adding 3 gives $\mu _ { z } = 3 \text { and } \sigma _ { z } ^ { 2 } = 4$

The probability that the RV Y that is uniformly distributed over [0,1) produces values that lie in the range [0.1, 0.5] equals _____.

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Question 4

An experiment with RV X produces three possible values 0, 1 and 2.If the probability $P [ X = 0 ] = 0.4$ and $P [ X = 1 ] = 0.3 , P [ X = 2 ] =\_\_\_\_\_\_$

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Question 5

The standardized Gaussian PRNG produces Gi and If G1 and G2 are independent standardized Gaussian RVs and $\mathrm { Z } = 2 \mathrm { G } 1 + 3 \mathrm { G } 2$ the value of the variance of P equals______.

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Question 6

The PRNG value Yiis uniformly distributed over [0,1).The value $Z _ { i } = 2 Y _ { i } + 3$ is uniformly distributed over what range?

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Question 7

For the RV Z that is uniformly distributed between -2 and 4, the mean $\mu _ { z } =\_\_\_\_\_\_$

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Question 8

When performing 10 experiments the RV X produces the following realizations:2, 1, -1, 0, 3, 5, -1, 2, 0, 1 Ave(X) = _ and Var(X) = _.

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Question 9

The standardized Gaussian PRNG produces Gi and the PRNG value $Y _ { i }$ is uniformly distributed over [0,1).If $\mathrm { G } _ { i } \text { and } Y _ { i }$ are independent, what is the mean and variance of $Z _ { i } = 2 G _ { i } + 4 Y _ { i } - 1$

The RV Z is uniformly distributed between -0.15 and 0.35 .What is the amplitude of PDF $p _ { z } ( x )$ that makes the area under the curve equal to 1.

The standardized Gaussian PRNG produces Gi .What is the mean and variance of $Z _ { i } = 2 G _ { i } + 3$

The probability that the RV Y that is uniformly distributed over [0,1) produces values that lie in the range [0.1, 0.5] equals _____.

An experiment with RV X produces three possible values 0, 1 and 2.If the probability $P [ X = 0 ] = 0.4$ and $P [ X = 1 ] = 0.3 , P [ X = 2 ] =\_\_\_\_\_\_$

The standardized Gaussian PRNG produces Gi and If G1 and G2 are independent standardized Gaussian RVs and $\mathrm { Z } = 2 \mathrm { G } 1 + 3 \mathrm { G } 2$ the value of the variance of P equals______.

The PRNG value Yiis uniformly distributed over [0,1).The value $Z _ { i } = 2 Y _ { i } + 3$ is uniformly distributed over what range?

For the RV Z that is uniformly distributed between -2 and 4, the mean $\mu _ { z } =\_\_\_\_\_\_$

When performing 10 experiments the RV X produces the following realizations:2, 1, -1, 0, 3, 5, -1, 2, 0, 1 Ave(X) = _ and Var(X) = _.

Introduction

Sensors and Actuators

Combinational Logic Circuits

Sequential Logic Circuits

Converting Between Analog and Digital Signals

Detecting Data Signals in Noise

Designing Signals for Multiple-Access Systems

Source Coding

Channel Coding

Data Networks

Symbology

Excel Best Practices

Filters

Exam 6: Modeling Random Data and Noise

The RV Z is uniformly distributed between -0.15 and 0.35 .What is the amplitude of PDF pz(x)p _ { z } ( x )pz​(x) that makes the area under the curve equal to 1.

The standardized Gaussian PRNG produces Gi .What is the mean and variance of Zi=2Gi+3Z _ { i } = 2 G _ { i } + 3Zi​=2Gi​+3

The probability that the RV Y that is uniformly distributed over [0,1) produces values that lie in the range [0.1, 0.5] equals _____.

An experiment with RV X produces three possible values 0, 1 and 2.If the probability P[X=0]=0.4P [ X = 0 ] = 0.4P[X=0]=0.4 and P[X=1]=0.3,P[X=2]=______P [ X = 1 ] = 0.3 , P [ X = 2 ] =\_\_\_\_\_\_P[X=1]=0.3,P[X=2]=______

The standardized Gaussian PRNG produces Gi and If G1 and G2 are independent standardized Gaussian RVs and Z=2G1+3G2\mathrm { Z } = 2 \mathrm { G } 1 + 3 \mathrm { G } 2Z=2G1+3G2 the value of the variance of P equals______.

The PRNG value Yiis uniformly distributed over [0,1).The value Zi=2Yi+3Z _ { i } = 2 Y _ { i } + 3Zi​=2Yi​+3 is uniformly distributed over what range?

For the RV Z that is uniformly distributed between -2 and 4, the mean μz=______\mu _ { z } =\_\_\_\_\_\_μz​=______

When performing 10 experiments the RV X produces the following realizations:2, 1, -1, 0, 3, 5, -1, 2, 0, 1 Ave(X) = _____ and Var(X) = _____.

Introduction

Sensors and Actuators

Combinational Logic Circuits

Sequential Logic Circuits

Converting Between Analog and Digital Signals

Detecting Data Signals in Noise

Designing Signals for Multiple-Access Systems

Source Coding

Channel Coding

Data Networks

Symbology

Excel Best Practices

Filters

The RV Z is uniformly distributed between -0.15 and 0.35 .What is the amplitude of PDF $p _ { z } ( x )$ that makes the area under the curve equal to 1.

The standardized Gaussian PRNG produces Gi .What is the mean and variance of $Z _ { i } = 2 G _ { i } + 3$

An experiment with RV X produces three possible values 0, 1 and 2.If the probability $P [ X = 0 ] = 0.4$ and $P [ X = 1 ] = 0.3 , P [ X = 2 ] =\_\_\_\_\_\_$

The standardized Gaussian PRNG produces Gi and If G1 and G2 are independent standardized Gaussian RVs and $\mathrm { Z } = 2 \mathrm { G } 1 + 3 \mathrm { G } 2$ the value of the variance of P equals______.

The PRNG value Yiis uniformly distributed over [0,1).The value $Z _ { i } = 2 Y _ { i } + 3$ is uniformly distributed over what range?

For the RV Z that is uniformly distributed between -2 and 4, the mean $\mu _ { z } =\_\_\_\_\_\_$

When performing 10 experiments the RV X produces the following realizations:2, 1, -1, 0, 3, 5, -1, 2, 0, 1 Ave(X) = _ and Var(X) = _.