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 ...

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.

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 ...

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 ...

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].

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 ...

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 ...

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)?

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 ...