Suppose that a manufactured product has 2 defects per unit of product inspected. probabilities of finding a product without any defect, 3 defects, and 4 defects. (Given e Using Poisson's distribution, calculate the e-2 =0.135)
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- Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15A random sample of size 225 is taken from a population with a mean of 10 and variance 4. Find the probability that the sample mean is greater than 9.8 but less than 10.2.The geometric distribution gives the probability that the first success occurs at the xth trial with success probability p. f(x)=(1-p)x-1p, x=1,2,3,... Show that E(X)=1/pA technician suspect that the number of computer errors recorded per day in the LAN follows a Poisson distribution with a mean of 2 errors per day. Record of the number of errors per day for the past 260 days are shown in table below. Number of Number of Pr(X = x) E (0; – e;) Errors per days ei day 77 1 90 2 55 3 30 4 or more a. Test the hypothesis that the number of computer errors per day has the Poisson distribution with mean 2 at the 5% significance level. b. Find an approximate value of the p – value for the test statistics in (a). 8Losses come from a mixture of an exponential distribution with mean 100 with probability p and an exponential distribution with mean 10,000 with probability 1– p. Losses of 100 and 2000 are observed. Determine the likelihood function of p. -0.01 pe (1– p)e“ pe 20 (1– p)e0² -0.2 (A) 100 10,000 100 10,000 pe (1– p)e“ -0.01 (B) pe (1– p)e02' 100 10,000 100 10,000 pe, (1- p)e0. 20 (1– p)eº -0.01 pe 100 -0.2 (C) pe 10,000 100 10,000 pe, (1- p)e 00i -0.01 (D) -20 ре (1– p)e02 100 10,000 100 10,000 e 0.01 +(1– p) e -20 (E) р. 100 10,000 100 10,000Exercise 5.4 A lot of 75 washers contains 5 defectives whose variability in thickness is unacceptably large. A sample of 10 washers is selected at random without replacement. 1. Determine the probability mass function of the number of defective washers (X) in the sample. 2. Find the probability that at least one unacceptable washer is in the sample. 3. Calculate the mean and variance of X.Suppose x is a normally-distributed random variable with mean µ= 50 and standard deviation o=2. Use the table to find the probability that x>55. Express your answer as a decimal. -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2.5 Area 0.01 0.02 0.07 0.16 0.31 0.5 0.69 0.84 0.93 0.98 0.99 0.01 с. 0.64 а. d. 0.99 b. 0.98Can you help with part b without using Chebyshev's theoremSuppose X is a normal distribution random varible with u=33 and o=9. Find the value of xo of the random variable x for parts a, b, c, and, d.Assume that daily evaporation rates (E) have a uniform distribution with a = 0 and b = 0.35 inches/day. Determine the following probabilities:Pr (E ≥0.1) Pr (E ≤ 0.22) Pr (E = 0.2) Pr (0.05 ≤ E ≤ 0.15Assuming a population is normally distributed, calculate the probability that a random member of the population falls between 3 standard deviations below the mean and 1 standard deviation below the mean. In other words in mathematical notation: P(-3 < z < -1) Enter your answer in decimal form. For example, 75% should be entered as 0.75.I need to figure out the probability that component proportions produce the results X1 < 0.2 and X2 > 0.5 but I need help.SEE MORE QUESTIONS