Problem #3: Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitudetest. Suppose the pdf of X isProblem #3(a):Problem #3(b):f(x; 0) =(0+1)x00 ≤ x ≤ 1otherwisewhere > -1. A random sample of ten students yields the data0.42, 0.60, 0.57, 0.67, 0.80, 0.59, 0.70, 0.53, 0.96, 0.51(a) Use the method of moments to obtain an estimator for 0, and then use it to compute an estimate from the data.(b) Find the maximum likelihood estimator for 0, and then use it to compute an estimate for from the data.answer correct to 2 decimalsanswer correct to 2 decimals

Data : 0.42, 0.60, 0.57, 0.67, 0.80, 0.59, 0.70, 0.53, 0.96, 0.51

Answered: Problem #3: Let X denote the proportion…

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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1
Problem 1. Suppose that X ~ N(3,0.16). Find the following probabilities. (1). Р(X > 3) (2). P(X > 3.3) (3). Р(2.8 < X <3.1) (4). Find the 98-th percentile of X. (5). Find the value c such that P(3 – c < X < 3+ c)=0.9.
Problem 1. Let x be the level of precaution, w=16 is the marginal cost of precaution, p(x)=1/x is the probability of an accident, and A=10,000 is the cost of an accident. Find the efficient precaution level.
9.
Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of discovering the disease in 97% of all afflicted individuals. Suppose further that when it is tried on healthy individuals, 5% of them are incorrectly diagnosed as having the disease. Finally, suppose that when it is tried on individuals who have certain other milder diseases, 10% of them are incorrectly diagnosed. It is known that the percentages of individuals of the three types being considered here in the populations at large are 1%, 96%, and 3%, respectively. Calculate the probability that an individual, selected at random from the population at large and tested for the rare disease, actually has the disease if the test indicates he is so afflicted.
Problem 5.2.: The daily wage of a particular industry is normally distributed with a mean of 150 pesos. In a random sample of 144 workers of a very large company in this industry, the mean daily wage was found to be 148 pesos with a standard deviation of 10 pesos. Can this company be accused of paying inferior wages (less than the usual) at α=5%? Please Refer to Problem 5.2.: Question: The decision rule to be used at α=5% is: “Reject Ho of tc > ttab = 66, otherwise fail to reject Ho.”
Problem 11. (5 points) Use normal approximation to estimate the probability of getting at most 55 girls in 100 births. Assume that boys and girls are equally likely.
Problem #4: (2 points) Find a 100(1 - a)% confidence interval for 0, given X₁,,X, i.i.d. with pdf f(x0) = 1,0-0.5 0.
Problem #2: Death for (x) is distributed such that the probability that an individual dies in the next 3 months is always the same regardless of their age. The probability that (x) will survive for 5 years is 35.8486%. What is the APV (the EPV) of the payout of a 1.5 year term life insurance policy on (x) if it pays $100,000 at the end of a quarter in which (x) dies? Use an annual interest rate of 9% compounded monthly (that's not a typo; I am giving you the monthly rate). Problem #2: answer correct to the nearest dollar
Problem 9
Example 17: If P (x) = 0.1 x ,x= 1, 2, 3, 4 = 0 %3D *, otherwise find (i) P{X=1 or 2 } (ii) P

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