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Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 95% of all fasteners pass an initial inspection. Of the 5% that fail, 20% are so seriously defective that they must be scrapped. The remaining fasteners are sent to a recrimping operation, where 40% cannot be salvaged and are discarded. The other 60% of these fasteners are cor- rected by the recrimping process and subsequently pass inspection.
a. What is the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping?
b. Given that a fastener passed inspection, what is the probability that it passed the initial inspection and did not need recrimping?
the true mean breaking strength of yarn used in manufacturing drapery material is required to be above 100 psi. from
Consider the linear transformation T : complex numbers^n -> complex numbers^n given by T( z1, z2, ... , zn ) = ( a1z1, a2z2, ... , anzn). What is the dimension of the subspace spanned by the eigenvectors of T? Exhibit a basis for this space, and g..
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Suppose we fit the model y = X1β1+ ε when the true model is actually given by y = X1β2 + X2β2 + ε. For both models, assume E(ε) = 0 and Var(ε) = σ2I. where I is the identity matrix. Find the expected value and variance of the ordinary least-squares e..
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