problem 1: State the term marginal densities.
problem 2: Describe the conditional PDF and its respective properties.
problem 3: Define mean or average or expected value of a random variable. Describe how it is computed for continuous and discrete random variables.
problem 4: Describe variance and standard deviation of the random variable.
problem 5: Define random process and describe ensemble and sample function.
problem 6: Describe ensemble and time averages.
problem 7: Describe the stationary random procedure with the help of one illustration.
problem 8: Illustrate the term ergodic process. Describe the difference between ergodic and stationary process.
problem 9: A box includes 2 White, 3 black and 4 Red balls. Three balls are drawn in succession. Determine the probability that they are of:
a) Different colors
b) Same color.
problem 10: Two fair dice are thrown. X symbolizes the total of the number of the two dice. Determine the probability function and distribution function of X.