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 monthsRecent 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…Suppose that the probability of a successful optical alignment of an optical data storage product is 0.8. Assume that the trials is independent. a. Determine the probability mass function of the number of trials (X) required until the first successful alignment. b. Find the probability that the first successful alignment requires four trials at the maximum c. Calculate the mean and variance of X
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- A dairy farmer accidentally allowed some of his cows to graze in a pasture containing weeds that would contaminate the milk from this herd. The farmer estimates that there’s a 10% chance of a cow grazing on some of the flavorful weeds. (a) Under these conditions, what is the probability that none of the 12 animals in this herd ate the tasty weeds? (b) Does the Poisson model give a good estimate of the probability that no animal ate the weed?(a) A structure consists of 100 column footings. Suppose the settlement of eachfooting is exponentially distributed with a mean of 2 inches and the settlementsbetween footings are statistically independent. What is the probability that themaximum settlement Smax among the 100 footings will not exceed 5.0 inches?Compare this exact probability with the answer obtained assuming an appropriateasymptotic distribution for Smax b. What is the probability that the minimum settlement Smax is at least 0.5 inches? c. Determine the mean and coefficient ofvariation of the maximum differential settlement delta(max) defined as (Smax-Smin)A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.141.14. A dietician is asked to test this claim and finds that a random sample of 2424 servings has a variance of 0.950.95. At alpha equals 0.10α=0.10, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed.
- Find the expected kinetic energy and the variance kinetic energy associated with a nail of mass m.Suppose that the relevant equilibrium model is CAPM with unlimited borrowing and lending at a riskless rate of interest. Compute the missing values (a*, b*, c*, d*, e*) in the following table, showing all intermediate steps. Expected Standard Residual Asset Return Deviation Beta Variance A 0.08 0.1 a* 0 B 0.12 b* 2 0.49 C c* d* 1 0 D 0.05 e* 0 0.36Consider the CAPM. The risk-free rate is 6% and the expected return on the market is 18%. What is the expected return on a stock with a beta of 1.3 when market is efficient?