An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by f(x) = { 3x-4, x>1 elsewhere (a) Verify that this is a valid pdf. (b) Find the cdf of X. (c) Find the average particle size in micrometers.

Q: y = In (x* + 5)³

A:

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A: To find the derivative of fx=x5e5x.

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A: We can find the tangent equation and normal equation as below.

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A:

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A: Solution

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A: We can solve this using Central difference formula f'(x) = (f(x+h) -f(x-h))/(2h)   The value of…

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A: The joint pdf for X and Y are given as:

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A:

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A:

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A:

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A:

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A: The marginal pdf of Y is right.

Q: Estimate the true percent relative error for the first derivative of the function, y =[en(x)]², at x…

A: We can solve this using Central difference formula f'(x) = (f(x+h) - f(x-h))/(2h)     x 0.95 1…

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A: By the property , the total probability density function is equal to one.