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- Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 1. n = 2, x = 2 n = 2, x = 0.Suppose X is binomially distributed with parameters n and p; further suppose that E(X) = 5 and Var(X) = 4. Find the n and p.Consider a binomial experiment with n=13 and p=0.2. A. Compute f(0) (to 4 decimals) B. Compute f(4) (to 4 decimals) C. Compute P(x less than or equal to 2) (to 4 decimals) D. Compute P(x greater than or equal to 3) (to 4 decimals) E. Compute E(x) ( to 1 decimal) F. Computer Var(x) and σ (to 2 decimals)
- Consider a binomial experiment with n=10 and p=0.3 a. compute p(x greater than or equal to 1) to 4 decimals b. Compute E (x) to 4 decimals c. P(x greater than or equal to 2) to 4 decimals d. Compute Var (x) and theta to 4 decimalsConsider a random sample X1,...,Xn,... ∼ iid Beta(θ,1) for n > 2. Prove that the MLE and UMVUE are both consistent estimators for θI got MLE = n/-∑logXi and UMVUE = (n-1)/∑logXi. Need help in proving consistencyConsider a binomial experiment with n = 20 and p = 0.4. Calculate the P(X ≥ 10). Do not usenormal approximation.
- Why is n> 3 significant here?Consider a binomial experiment with n=8 and p=0.5 . a. Compute f (0) (to 4 decimals). b. Compute (4) (to 4 decimals). c. Compute (x less than or equal 1 ) (to 4 decimals). d. Compute (x greater or equal 2 ) (to 4 decimals). e. Compute E(x) (to 1 decimal). f. Compute Var(x) and σ . (to 2 decimals) (to 2 decimals)Suppose N=10 and r=3 . Compute the hypergeometric probabilities for the following values of and . If the calculations are not possible, please select "not possible" from below drop-downs, and enter 0 in fields. Round your answers, if necessary. a. , (to 2 decimals). b. , (to 3 decimals). c. , (to 4 decimals). d. , (to 2 decimals). e. , (to 2 decimals).
- Suppose X1, X2, ... , Xn is a random sample and Xi = {1, with probability p 0, with probability 1-p} for every i = 1, 2, ... , n. Find the Moment Generating Function of ∑i=1n Xi . What is the distribution of ∑i=1n Xi ?Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)…Consider a binomial experiment with n=20 and p=0.70. Compute P(x>- 16) (to 4 decimals). Compute P(x>- 15) (to 4 decimals).