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- A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts the lot of N₁ + N₂ = 25 bulbs if the number of defectives, X among n = 5 items taken at random and without replacement from the lot is less than or equal to 1. The operating characteristic curve is defined as the probability of accepting the lot, namely OC (p) = P(X ≤ 1) = P(X = 0) + P(X = 1), where p = N₁/25 is the probability of a bulb being defective. (a) Show that the probability of the picking exactly X defectives follows a hypergeometric distribution. (b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 and p = 0.16. (c) Plot, using R, the operating characteristic curve for N₁ = 1 to N₁ = 4.A docs.google.com/forms/d/e (1) Let X be a random variable with p.d.f. fx) =- , then O.w (b) k- (0) k = (a) k=1 (d) k-5 (e) None of these a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer (2) Let X be a random variable with a function x= 0,1, 2,3 4 x! (3-x)! f(x) = , then p(x<1) is 0.w (b) (d) (e) None of these 27 (a) 27 (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer11. Assume that X is a uniform random variable on the interval [-22, 14. (a) tion of its mean. In other words, compute Find the probability that X is within two standard devia- P(µ – 20 < X < µ +2o). -
- 2. Let X, X,.., x, be a random sample from a distribution with p.d.f. f(x;0)=0x, |>x>0 Is the MLE O EE of 0? AEE of 0?If X is uniform random variable on interval (2,7) then the expexted value of X equal 9/2 (1/2 5/2(1) Let X be a random variable with p.d.f. ke 3 0Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON