4-52. If f(x) =e ,- co

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Answered: 4-52. If f(x) =e *,- 0

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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An article suggests the uniform distribution on the interval (8.5, 18) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? X < 8.5 F(x) = 8.5 < x < 18 18 < X (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.) (d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.) What is the probability that the observed depth is within 2 standard deviations of the mean value?
Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately ?2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s2 = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?
Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the z-value for a score of 80? -2.0 -0.4 1.0 2.0 0.4
QI/ Experimental data for the heat capacity in cal/(g.mol)(°C) as a function of temperature is given as follow: Temperature (C) 3 7. Heat capacity 19.65 26.74 32.80 37.74 41.75 45.06 47.83 Fit the data to an empirical heat-capacity equation of the form [C, = a + bT + b;T), and compute the standard deviation.
Q.6 (a) Write the gamma distribution for a random variable X denoted by X~F(a, B); its mean, variance and moment generating function (No derivation is required). (b) What is the relationship between gamma distribution and chi-square distribution?
The average height X and weight Y of males in population have a bivariate normal distribution with means µX 1.80 m., µy 90.0 kgs and standard deviations Ox = 0.30 m., oy = 15.3 kgs respectively. The correlation coefficient between X and Y is p= 0.80.
Compute the standard score (Z-score) for x, when x = 21, the mean of the distribution = 27, and the variance (S2) = 9. Z = %3D O 2 -2 .67 -.67
How do you find the mean and variance of part(d)?I need the detailed solution.
Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s2 = 3.4. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. H0: σ2 < 5.1; H1: σ2 = 5.1H0: σ2 = 5.1; H1: σ2 < 5.1 H0: σ2 = 5.1; H1: σ2 > 5.1H0: σ2 = 5.1; H1: σ2 ≠ 5.1 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a exponential population distribution.We assume a normal population distribution. We assume a uniform population distribution.We assume a binomial population distribution. (c) Find or estimate the P-value…
I For Poisson's distribution prove that Variance =
nN(dp) is define as the “number distribution function” , where dp is the particle diameter. Assume nN(dp) is a normal distribution with a mean of 10 µm and a standard deviation of 2 µm. The total number concentration of particles of all sizes is 10,000 particles cm-3. What is the number concentration of particles in the size range 10 µm and 14 µm?
Which of the following statement is INCORRECT? If Y, follows the standard normal distribution and Y, follows a chis-square distribution with degrees of freedom n, then nY/Y t distribution. If X1,.., Xn is a random sample from a normal population with population mean 1 and variance 1, then (X -1) + (X - 1 (X, - 1) follows a chi-square distribution with degrees of freedom n. If X,..., Xn is a random sample from a normal distribution with population mean 0 and a known variance o, then must follow a distribution, where X denotes the sample mean and S denotes the sample standard deviation. If T follows at distribution with degrees of freedom n, then T must follow an F distribution with degrees of freedom 1 and n.

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