Exercise 5.2 Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.8. Assume that the trials are independent. 1. Determine the probability mass function of the number of trials (X) required until the first successful alignment. 2. Find the probability that the first successful alignment requires four Trials at the maximum. 3. Calculate the mean and variance of X
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- 1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given monthsThe germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…Recent studies have shown that Punica granatum (or pomegranate) seeds have germination time that is found to be normally distributed. To verify this, a biologist measured the number of days to germination of 20 random pomegranate seeds. Below shows the data obtained: 15.82 16.69 17.69 18.14 19.38 16.07 16.89 17.98 18.33 19.48 16.49 17.30 18.10 18.50 19.55 16.67 17.67 18.11 19.35 20.66 Using visual inspection with the given histogram and Q-Q Plot below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution? Explain by interpreting each graph. Figure 1. Histogram Figure 2. Q-Q Plot 2. Using the Wilk-Shapiro Test with R software output given below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution at ?=1%? Complete the following steps: Shapiro-Wilk…
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