5. The random variable X is the shear strength of a weld. It is known that X has a normal distribution with mean and variance o2. A random sample of 10 observations is taken yielding the following data (in psi): 392 376 401 367 389 362 409 415 358 375 (a) The maximum likelihood estimators for u and o² were shown in class to be Σ₁(X₁-X)² n û = X and respectively. Compute the maximum likelihood estimates of u and o² with the data given. Use the Statistics mode in your calculator. Watch the video on "Univariate Statistics with Casio Calculator" on Moodle for your calculator. (b) Recall that Þ(z) = P(Z ≤ z) where Z~ N(0, 1). Express P(X ≤ 350) as a Þ(.). (c) Use the invariance principle to find the maximum likelihood estimate of P(X ≤ 350). (d) Find the maximum likelihood estimate of the strength below which 90.15% of all welds will have their strengths. Round your answer to 2 decimal places.
5. The random variable X is the shear strength of a weld. It is known that X has a normal distribution with mean and variance o2. A random sample of 10 observations is taken yielding the following data (in psi): 392 376 401 367 389 362 409 415 358 375 (a) The maximum likelihood estimators for u and o² were shown in class to be Σ₁(X₁-X)² n û = X and respectively. Compute the maximum likelihood estimates of u and o² with the data given. Use the Statistics mode in your calculator. Watch the video on "Univariate Statistics with Casio Calculator" on Moodle for your calculator. (b) Recall that Þ(z) = P(Z ≤ z) where Z~ N(0, 1). Express P(X ≤ 350) as a Þ(.). (c) Use the invariance principle to find the maximum likelihood estimate of P(X ≤ 350). (d) Find the maximum likelihood estimate of the strength below which 90.15% of all welds will have their strengths. Round your answer to 2 decimal places.
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 the random variable X denote the shear strength of a weld.
The sample of 10 observations is given as follows:
392 376 401 367 389 362 409 415 358 375
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