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- 4. Given a binomial distribution X~b(n,p) with parametersn = 50 and p = 5%. a) Determine the mean and the standard deviation.Suppose that W is a (a = 3, 3 = })-gamma random variable and N is a µ = -Poisson random variable independent of W. What is E (w*]? un for u-Poisson random variable N. n! Note: PN (n) = P (N = n) = e Hint: pmf for a (r, p)-negative binomial random variable is given by n - n = r,r + 1,... r - 112. Suppose (1, 2, ..., n) is a random sample from ...,n) is a random sample from a normal distribution, find the absolute efficiency of the maximum likelihood estimator of 0 if, x; ~ ~ N(0, 1).
- Suppose that X is a binomial random variable with n=300 and p=0.5. Is the normal approximation reasonable? * Yes No Find the probability P(x is less than or equal to 70)based on the approximate normal distribution. * Your answer Find the probability P(x is less than or equal to 70)based on the corresponding binomial distribution. * Your answer4- Binomial Probability Distributions Due 03-13-2022 - Students.docx (18.6 KB) 4. A coin is flipped 8 times. Calculate the mean, variance and standard deviationA two-sided test of hypothesis assumes that a normally distributed random variable X with mean of 102.83 and standard deviation of 12.23 with alpha - 5% for a sample of size 4. If the real mean is 115 compute the power of the test.
- A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3; Are the sampling distribution of the sample mean with n = 26 and n = 52 normally distributed? Also calculate the probabilities that the sample mean is less than 18.6 for both sample sizes.Find these probabilities for a standard normal random variable Z. Be sure to draw a picture to check your calculations. Use the normal table or software. (a) P(Z - 1.1) (c) P(|Z| 0.7) (e) P(- 1.15Z - 1.1)= (Round to four decimal places as needed) (c) P(|Z| 0.7) = (Round to four decimal places as needed.) (e) P(-1.1sZ 12) =| (Round to four decimal places as needed )The probability that a trainee will remain with a company is 0.6. the probability that am employee earnsbmore than k10,000 per month is 0.5. the probability that an employee who is a trainee remained with the company or who earns more than k10,000 per month is 0.7. what is the probability that an employee earns more than k10,000 per month given that he is a trainee who stayed with the company
- 6.)A random sample of size 121 is taken from a population in which the proportion with the characteristic of interest is p = 0.47. Find the indicated probabilities. P(p ^≥0.50)no. 2For a uniform random variable U∼U(5,26)U∼U(5,26), find the probability P(U>14)P(U>14): P(U>14)=P(U>14)= (Round the answer to 4 decimal places)