Probability : k-out-of-n System

Related BrainMass Solutions

• Probability of k-out-of-n Systems

  23846 Probability of k-out-of-n Systems 2.16) Consider the k-out-of-n system (info on the system: A system consists of n independent components. Each component functions with probability p.

• Chevalier de Mere's puzzle and other questions of probability

  If the ith component functions with probability pi, compute the probability that a 2-out-of-4 system is functioning. b. Repeat (a) for a 4-out-of-5 system. c. Repeat (a) for a k-out-of-n system, when all pi's are equal to p. 4.

• Internal energy and entropy of a two level system

  The general formula for the average of the total energy of the system is: E(N) = -d Log[Z(N)]/dbeta (4) To see this, let's work out the derivative (I'm suppressing the argument N of Z for the moment): d Log(Z)/dbeta = 1/Z dZ/dbeta

• Probability theory

  Now we only need to take k steps out of 2k to be left steps, there are C(2k, k) choices. So the probability that the person comes back to the same tree is C(2k, k) * (1/2)^k * (1/2)^k = ((2k)!/(k!*k!))

• Probability: Acceptance Sampling

  Hence, likelihood of acceptance == probability that 0 defective or 1 defective in the sample of 20, P(0 or 1) = P(0) + P(1) In Binomial distribution, probability of r defective out of n, P(n,r) = C(n,r) * p^r * q^(n-r) Hence, P(0 or 1) = P(

• Two Probability Questions

  If you design for two settings, there will be two trials n = 2 1 out of 5 will be unsafe p = 1/5 = 0.2 If you design for one setting, there will be one trial n = 1 2 out of 5 will be unsafe p = 2/5 = 0.4 So, plugging those into the equation

• Probability and Statistics: Coin Flipping Project

  The formula is : P(k out of N) = N!/[k!(N-k)!]

• Binomial Coefficient and Factorial Notation

  (n choose k) p^k (1-p)^n-k where p is the probability of "success" and (1-p) is the probability of "failure". So, lets see an example... We want to find the probability of rolling at least 1 six in 4 rolls of a single die.

• Queueing Systems

  Taking out (alpha^n) and (n-1)! out of the integral, and joining t and t^(n-1) gives: E(T) = alpha^n inf ---------- integral (t^n)*exp(-alpha*t) dt (n-1)!