Exercise 2.37 If X has the binomial distribution with parameters n and p- 1-q, show that...
Let X be random variable with the binomial distribution with parameters n and 0 < p < 1. (1) Show that (P(X = x) / P(X = x -1)) - 1 = np + (p - x)) / (x(1-p)) for any 1 ≤ x ≤ n. (2) Show that when 0 ≤ x < (n + 1)p , P(X = x) is an increasing function x and for (n + 1)p < x ≤ n, P(X = x) is a...
Q 4. Let X has a binomial distribution with parameters n and 0. (a) For what value of 0 is the probability function of X a maximum? (b) Find the mean and variance of X.
Suppose that x has a binomial distribution with n = 200 and p = 0.42. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (o) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x. np n(1 – p) Both np and n(1 – p) (Click to select) A 5...
Suppose that x has a binomial distribution with n = 198 and p = 0.44. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (o) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x пр n(1 - p) Both np and n(1 – p) (Click to select) A 5...
Suppose that x has a binomial distribution with n = 198 and p = 0.41. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (σ) to 4 decimal places.) A) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x. np n(1 – p) Both np and n(1 – p) large/smaller than 5 B) Make...
Let X be a random variable, which has a binomial distribution with parameters n and p. It is known that E(X) = 12 and Var(X) = 4. Find n and p.
Exercise 1: Let Y be a binomial distribution of parameters n = 10 and p = 0.4. Determine the normal approximation for: a) P (Y ≥ 7) Exercise 2: The quality control of an automobile manufacturer accuses 1% of failures in the process of antioxidant protection of bodywork of the vehicles it produces. Calculate the probability that: a) none of the 100 vehicles ordered by a dealership has the aforementioned failure; b) only one vehicle has the fault mentioned in...
Please answer as neatly as possible. Much thanks in advance! 7. If Y has a binomial distribution with parameters n and p, consider p = (Y + 1)/(n+2) as an estimator of p. Is p a consistent estimator for p? Is p an asymptotically unbiased estimator for p? 7. If Y has a binomial distribution with parameters n and p, consider p = (Y + 1)/(n+2) as an estimator of p. Is p a consistent estimator for p? Is p...
Suppose that x has a binomial distribution with n = 50 and p = .6, so that μ = np = 30 and σ = np(1 − p) = 3.4641. Calculate the following probabilities using the normal approximation with the continuity correction. (Hint: 26 < x < 36 is the same as 27 ≤ x ≤ 35. Round your answers to four decimal places.) (a) P(x = 30) (b) P(x = 26) (c) P(x ≤ 26) (d) P(26 ≤ x ≤ 36) (e) P(26...
Consider the binomial distribution with parameters n 10 and p (unknown) a) Is this binomial distribution an exponential family distribution? b) Find a sufficient statistic for p.