7. Suppose that ladybugs are distributed randomly and uniformly on the leaves of apple trees at arate of i per tree. In an orchard of 100 trees, 58 contained no ladybugs, and 42 contained one ormore ladybugs. What is the maximum likelihood estimate of 2?Hints: There are two different distributions involved in this question, and you will need to use theInvariance Property.A)0.42B)0.58C)0.545D)4.060

Number of trees in which ladybugs are present in an orchard of 100 trees, so, The maximum…

Answered: 7. Suppose that ladybugs are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 15 17 17 20 15 12 13 16 15 12 State the null and alternate hypotheses. H0: ? = 14; H1: ? < 14 H0: ? > 14; H1: ? = 14 H0: ? < 14; H1: ? = 14 H0: ? = 14; H1: ? ≠ 14 H0: ? = 14; H1: ? > 14 What is the value of the sample test statistic? (Round your answer to three decimal places.)
3. The following observed claim frequency data is collected over a period of 365 days by the XJTLU insurance company: Number of Claims per Day Observed Number of Days 0 50 122 101 1 2 3 4+ 92 0 As a junior data analyst in this company, you are asked to complete the following task by your manager: (a) Fit a Poisson distribution to the above data, using the method of maximum likelihood. (b) Group the data by number of claims per day into four groups: 1 2 3 3 or more Apply the chi-square goodness-of-fit test to evaluate the null hypothesis that the claims follow a Poisson distribution. Determine the result of the chi-square test.
2. Let the random variables Y, Y,, ...,Y, be normally distributed with mean 10 and variance 4. Find a valuek such that Σ ;- 10 2
None
5. Suppose that a student attending a class has an infectuous disease. Suppose that with probability 1/2 she does not infect anybody, with probability 1/4 she infects exactly one other person, and with probability 1/4 she infects exactly two people. Let X be the number of people infected by this student. Calculate the expectation and the variance of X.
5. The meat department at a local supermarket specifically prepares its "1-pound" packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1 pound. Suppose that the weights of these "1-pound" packages are normally distributed with a standard deviation of 0.15 pound. What is the probability that a randomly selected package of ground beef will weigh less than 0.80 pound?a. 0.2088b. 0.9088c. 0.0918d. 0.4088
9. This is a simplified inventory problem. Suppose that it costs c dollars to stock anitem and that the item sells for s dollars. Suppose that the number of items thatwill be asked for by customers is a random variable with the frequency functionp(k). Find a rule for the number of items that should be stocked in order tomaximize the expected income. (Hint: Consider the difference of successiveterms.)
Let X1,..., X be an independent trials process with common expected value 2 and common variance 17. What is the exact value of the expected value of the average A? What is the variance of the average An? Your formula should have n. According to the Chebyshev inequality, P(An 20.2) ≤ (your formula should have n) Using your bound from the Chebyshev inequality, how many trials are needed so that P(An 2≥ 0.2) 0.91? (see the note below here) If you get an answer like n > 123.8, round it up to the next whole number: Your response: 124
Q.2 Listed is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous. ilitu distrib blo llowe
Q2] As shown in the table below that gives the age distribution of individuals starting new university employments. Find the following probabilities: 1-Ages (28-39). 2- Age>55. 3-Age<35. N:15 G:2 R=30 15-24 25-34 35-44 45-54 320-R 420+R| 315 55-64 Age Frequency 65-74 120 250 220-R

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