Exercise 5:Suppose you have a random sample X1, X1,,X, where:X 1 if a randomly selected student uses a car to commute to campusX = 0 if a randomly selected student does not use a carAssuming that the X, are independent Binomial B(1,p) random variables withunknown parameter p.Using the method of moments, describe how you would findan estimator of p, the proportion of students who use a car, from the randomsample. Denote this estimator with p. When is the variance of the estimatorlarger for a sample size 10, or for a sample size 100? An estimator is unbiased, ifEP = p. Is your estimator unbiased?

Given information: Given that the ransom sample X1, X2, … , Xn are binomial random variables.

Answered: Suppose you have a random sample X1.…

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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Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 10 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. If one car is randomly chosen, find the probability that it is traveling more than 78 mph. If one of the cars is randomly chosen, find the probability that it is traveling between 79 and 85 mph. 85% of all cars travel at least how fast on the freeway? mph.
the height of a randomly selected male individual in a population is a normal random variable with mathematical expectation m=178 σ =8 what % of the individuals of this population is taller than 185cm?the height of the female individuals in this population is of normal distribution with parameters m=165 cm and σ=7cm. what % of the women are taller than half of the men
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where appropriate. 1. Experience has shown that the seeds from a certain variety of orchid have a 75% chance of germinating when planted under normal conditions. Suppose n seeds are planted, and let X be the random variable that counts the number of seeds that germinate. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) = = (b) What is the minimum value of n so that the probability of at least five of the seeds germinating is at least 90%?
В2. (a) Given the probability Venn diagram below for the two Events A and B find the probabilities: 0.6 0.5 A 0.2 (i) (ii) (iii) Pr( A 'OR' B) Pr( Not-A 'AND' Not-B) Pr( Not-A "OR' Not-B) (b) A random sample from a population of X with unknown mean but a known variance, o = 400, gives the following data: sample size, n= 125, Ex= 1750. (i) Give a point estimate of the population mean, u. (ii) Is this estimate biased or not. Give a reason. (ii) Derive a 95% confidence interval for the population mean, µ.
If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert - Formats - B A く) (b) Find the ZSCore for a trial lasting 20 days. (Round your answer to three decimal places.) (c) If one of the trials is randomly chosen, find the probability that it lasted at least 20 days. (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (b), rounded to one decimal place).
200 poodles 61 are left-paued left -pawed. a random sample of In a random sample ef 220 labradores 38 are Can we conclude that the difference in The tuo sample proportions of left pawed dogs is statistically significont for x= 0.05 ?
We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?
Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO
Total blood volume (in mi) per body wight (in ke) is important in medical research. For healthy aduks, the red blood cell volume mean is about p = 28 ml/kg.t Red blood cell vokume that is too lom ar too high can indicate a medical problem. Suppose that koger has had seven blood tests, and the red blood cell volumes weré as follows Let x be a random variable that represents Roger's red blood cll volume. Assume that x has a narmal distributian and - 4.75. Do the data indicate that koger's red blood cell valume is different (either way) from a- 28 mi/kg? Use a 0.01 lervel of significance. a What is the leval of sigaicance State the null and alternate hypotheses. Will you use a left-lailed, right-laded, or two-tailed test? O H: - 28 ml/kg; H: 2s m/kg; Ima-tailed o Ho: - 28 ml/ka; H 28 m/ka, let-tailed O Ho: 28 mil/kg: H1:- 28 ml/kg; tmo-tailed O Ho: 28 m/ka, H > 28 m/kg; right-laiked (b) What sampling distribution wil you use? Explain the rationale for your choice of sampling distributian.…

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