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An article considered the use of a uniform distribution with A = 0.20 and B = 4.25 for the diameter X of a certain type of weld (mm). (a) Determine the pdf of X.

User Zombaya
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1 Answer

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Final answer:

The PDF of the uniform distribution for the diameter X of a weld with given bounds A = 0.20 and B = 4.25 is a constant 0.2469 over that interval. The calculation step involves the reciprocal of the difference between B and A to find the uniform PDF value.

Step-by-step explanation:

The probability density function (PDF) of a continuous uniform distribution over the interval [A, B] is given by f(x) = 1 / (B - A) for A ≤ x ≤ B and f(x) = 0 otherwise. For the given uniform distribution with A = 0.20 and B = 4.25, we calculate the PDF as follows:

f(x) = 1 / (4.25 - 0.20) = 1 / 4.05 ≈ 0.2469.

Therefore, the PDF of the diameter X of the weld is constant over the interval [0.20, 4.25] and equals approximately 0.2469.

The correct calculation step is to subtract the lower bound A from the upper bound B to find the length of the interval, and then take the reciprocal of this length to find the uniform PDF value.

User Mohammadjh
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