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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

10. a. Xis a Gaussian random variable with EMI = 0 and Var(X) = 6. Evaluate P (X 10). b. Y is a Gaussian random variable with E[Y] = -2 and Var(Y) = 9. Evaluate Pa YI 11). c. Z is a Gaussian random variable with E121 = 5 and Var(Z) = 4. What approximate region contains 60% of the most likely values of Z?

10. a. Xis a Gaussian random variable with EMI = 0 and Var(X) = 6. Evaluate P (X 10). b. Y is a Gaussian random variable with E[Y] = -2 and Var(Y) = 9. Evaluate Pa YI 11). c. Z ...

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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

9. Yi and Y2 are independent continuous exponential random variables with A, and 22.X= max(YI,Y2). a. Find the CDF and PDF of X. b. Find the mean and variance of X.

9. Yi and Y2 are independent continuous exponential random variables with A, and 22.X= max(YI,Y2). a. Find the CDF and PDF of X. b. Find the mean and variance of X.

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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

8. A microcontroller can execute only one command at a time. Two commands are received 6 microseconds apart. The execution time for the first command is independent of the second and can be modeled as an exponential random variable with a mean of 5 microseconds. The execution of the second command can similarly be modeled as an exponential random variable with a mean of 10 microseconds. What is the expected time from the start of execution of the first command to the completion of the second command?

8. A microcontroller can execute only one command at a time. Two commands are received 6 microseconds apart. The execution time for the first command is independent of the second and can be modeled as an exponential random variable with ...

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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

7. II is a continuous uniform random variable taking values from -1 to 3. Y2 is an independent uniform random variables taking values from 0 to 4. Z= max(Yj, Y2). H= min(Y,, Y2). a. Find the CDF and PDF of Z. b. Find the mean and variance of Z. c. Find the CDF and PDF of H. d. Find the mean and variance of H.

7. II is a continuous uniform random variable taking values from -1 to 3. Y2 is an independent uniform random variables taking values from 0 to 4. Z= max(Yj, Y2). H= min(Y,, Y2). a. Find the CDF and PDF of ...

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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

6. Suppose continuous random variable X is uniformly distributed over [-2, 3] and Y=X2. a. Find the CDF and the PDF of Y. b. Find E[Y].

6. Suppose continuous random variable X is uniformly distributed over [-2, 3] and Y=X2. a. Find the CDF and the PDF of Y. b. Find E[Y].

electrical cumputers
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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

5. A certain casino game costs $1 to play and has an outcome of a loss with probability p, which nets $0 (a loss of the $1), or an outcome of a win with probability 1-p, which nets $2 (winnings of $1 + $1 from upfront cost). Each game costs exactly $1. a. What is the probability that a player starting with $1 will end up losing all winnings on exactly the Th game? Use p = 0.3. b. What is the probability that a player starting with $1 will end up losing all winnings in less than 10 games? Use p = 0.5. c. Find the probability that a player starting with $1 will lose all of their winnings eventually, as a function p. Plot your answer.

5. A certain casino game costs $1 to play and has an outcome of a loss with probability p, which nets $0 (a loss of the $1), or an outcome of a win with probability 1-p, which nets $2 (winnings ...

electrical cumputers
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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

4. The probability of a particular individual hitting the dart board in a particular throw is 0.8, independent of other throws. Z is the random variable representing the number of hits on target in 10 throws. a. Calculate and plot the PMF of Z. b. Calculate and plot CDF of Z. (You may desire to manually adjust the plot per convention) c. Using CDF values, find the probability that 3 < z < 6 throws were on target. d. Find E[Z] and var[Z]

4. The probability of a particular individual hitting the dart board in a particular throw is 0.8, independent of other throws. Z is the random variable representing the number of hits on target in 10 throws. a. Calculate and plot the ...

electrical cumputers
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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

3. A individual visits a large mango orchard with very large number of very large trees, where the probability of picking a ripe mango is p and is independent of other picked mangoes. The individual decides to pick ripe mangoes from single tree until an unripe mango is picked. If an unripe mango is picked, the individual changes trees. a. Let Ma the number of mangoes picked from the ith tree. What is the PMF, expectation value, and variance of Ma. b. Let Xi be the total number of ripe mangoes picked from i trees. What is the expected value and variance of X3. c. What is the joint PMF of XI and X2? d. Are M3 and X2 independent? Why?

3. A individual visits a large mango orchard with very large number of very large trees, where the probability of picking a ripe mango is p and is independent of other picked mangoes. The individual decides to pick ripe mangoes ...

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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

2. Consider the following joint distribution of random variables X and Y. Y a. Find Px(x). b. Calculate E[X]. c. Let Z = max(X,Y). Find Pz(z). d. What is E[Z]? e. Which value(s) ofy maximizes Var(XIY = Y)?

2. Consider the following joint distribution of random variables X and Y. Y a. Find Px(x). b. Calculate E[X]. c. Let Z = max(X,Y). Find Pz(z). d. What is E[Z]? e. Which value(s) ofy maximizes Var(XIY = Y)?

electrical cumputers
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venkyelectrical
venkyelectrical
Asked: May 24, 2022In: control systems engineering

1. A bad marksman takes 12 shots at a target with probability of hitting the target with each shot of 0.2, independent of other shots. Z is the random variable representing the number of hits. a. Calculate and plot the PMF of Z. b. Calculate and plot CDF of Z. (You may desire to manually adjust the plot for our convention) c. What is the probability that 3 < z < 6 shots were hits? d. Find E[Z] and Var[Z] e. If the marksman were to get $x for each shot on target. How much should the marksman expect to get, in order to break even on the $50 entry fee?

1. A bad marksman takes 12 shots at a target with probability of hitting the target with each shot of 0.2, independent of other shots. Z is the random variable representing the number of hits. a. Calculate and plot the ...

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