Questions from Operating Systems

Q: You are asked to play a game in which I hide a

You are asked to play a game in which I hide a prize in one of three boxes (with equal probability for all three boxes) while you are out of the room. When you return, you have to guess which box hide...

Q: Show that, all other things being equal, the greater the

Show that, all other things being equal, the greater the correlation coefficient of two random variables is, the greater the variance of their sum and the less the variance of their difference will be...

Q: Suppose X and Y each have only two possible values, 0

Suppose X and Y each have only two possible values, 0 and 1. Prove if X and Y are uncorrelated, then they are also independent.

Q: Consider a random variable X with the following distribution: Pr

Consider a random variable X with the following distribution: Pr[X= −1]=0.25;Pr[X=0]=0.5; Pr[X=1]=0.25. Let Y=X2. a. Are X and Y independent random variables? Justify your answer. b. Calculate the cov...

Q: An artificial example of a stochastic process is a deterministic signal x

An artificial example of a stochastic process is a deterministic signal x(t)=g(t). Determine the mean, variance, and autocorrelation of x(t).

Q: Suppose x(t) is a stochastic process with μ(

Suppose x(t) is a stochastic process with μ(t)=3 R(t1, t2)=9+4e −0.2| t1−t2 |.Determine the mean, variance, and covariance of the following random variables: Z=x(5) and W=x(8).

Q: Let {Zn} be a set of uncorrelated real-valued

Let {Zn} be a set of uncorrelated real-valued random variables, each with a mean of 0 and a variance of 1. Define the moving average Yn=∑i=0KαiZn−i for constants α0, α1, …, αK. Show that Y is stationa...

Q: What is the distinction between spatial locality and temporal locality?

What is the distinction between spatial locality and temporal locality?

Q: A patient has a test for some disease that comes back positive

A patient has a test for some disease that comes back positive (indicating he has the disease). You are told that the accuracy of the test is 87% (i.e., if a patient has the disease, 87% of the time,...

Q: A taxicab was involved in a fatal hit-and-run

A taxicab was involved in a fatal hit-and-run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are told that: 85% of the cabs in the city are Green and 15% are Bl...