Let and find given solution here we get that

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Unformatted text preview: m 5. The impact pressure of sea waves on coastal structures may be evaluated as , where is the horizontal velocity of the advancing wave and is a constant. Because of the uncertainty involved in the evaluation of variable; is is thus a derived variable from deviation , we consider this to be a random and has the normal pdf. Solution. Let . Assume has mean and standard with zero mean and unit variance and pdf . Now, Representing and by substituting in moment generating equation: So, Here to note that, using the transformation and also the area under the curve is unity. Taking the first derivative of the mgf at the origin, we can obtain the mean of as, Similarly, taking the second derivative, second-order moment of W is obtained as: Hence, the variance of W is: The mean of the required impact pressure follows immediately from the linear property of expectation as, Thus the variance is represents the coefficient of variation of horizontal velocity of the advancing wave , then the mean of which equals to The variance of , of can be obtained as: augmented by a factor which equals to augmented by a factor ....
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This note was uploaded on 03/18/2014 for the course CE 5730 taught by Professor Dr.rajibmaity during the Spring '13 term at Indian Institute of Technology, Kharagpur.

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