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Ceramic tiles are shipped in very large batches and an acceptance sampling procedure to monitor the number of cracked tiles in a batch has n=50 and c=10. Use the binomial approximation to calculate the probability of accepting the batch of tiles for various values of the proportion of cracked tiles p. Draw the operating characteristic curve.
Suppose that f: C->C and that f is analytic at a point z0 element of C. Prove that there exists a real number r>0 such that, the nth derivative of z0=[n!/(2 pi r^n)]x[int(e^(-niy)f(z0+re^(iy)) from 0 to 2pi with respect to y for all n element of N..
A beacon on a lighthouse 2000m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500m from P?
Let (X,d) be a compact metric space, and let Con(X) denote the set of contraction maps on X. We shall define the distance between two maps f,g which belongs to Con(X) as follows:
Important information about Cumulative Probability, Suppose the probabilities that a new car battery functions
Use Taylor's expansion to arrange the function in ascending order - explain briefly how the Taylor expansions tell you what order the functions
Find the correlation coefficient between X and Y. Is there a weak or strong, positive or negative correlation between X and Y?
Probability : Percentage of Defective Chips and Normal Distribution, A student needs 12 chips of a certain type to build a circuit. It is known that 5% of these chips are defective.
The aim of the project is to determine, for any fixed grid constants, an appropriate discrete skeletons from multivariate data so that the memory computational effort is minimal.
What are the probabilities of drawing a certain colour candy? Use the theoretical method to determine the probability of the given outcome or event.
Rate of change occurs in a side of a triangle with respect to the change occurs in another side - Find the rate it is dropping?
Using one of the tests for convergence (comparison, limit, integral, nth term, etc.), show whether the following series converges or diverges:
List all the binary relations on the set {0,1}. List the reflexive relations on the set {0,1}.
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