# 2 quotient of two random variables the expression for

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Unformatted text preview: tes is also a log-normal variate. n Let, Z X i where, X i ’s are statistically independent log-normal random variables with i 1 parameter, X i and X i . n Now if, ln Z ln X i where X i ’s are normal variates, then Z is also mean and variance i 1 as given, n n 2 Z E ln Z X and Z Var ln Z X respectively. i 1 i i 1 i Hence Z is also follows log-normal distribution having parameters, Z and Z . 6. Solved Problems of One Function of Two Random Variables Problem 3. The settlement of a footing on sand may be estimated on the basis of the theory of elasticity as given by, S PBI M where, S =footing settlement in m. P =average applied bearing pressure in tons per sq. m. B =smallest footing dimension in m. I =influence factor, depending on footing Geometry, depth of embedment, depth to reach hard stratum, and M =Modulus of compressibility Let P , B , I , M are independent log-normal variates with parameters, P ,B ,I ,M and P , B , I , M respectively. The values of mean and coefficient of variation used for the design is shown in table given below. Parameters P (tons/m2) B (m) I M (tons/m2) Mean 1.2 5.5 0.5 30.0 Coefficient of Variation 0.09 0.02 0.12 0.15 a. Determine the mean settlement of the footing and its coefficient of variation b. If the maximum allowance settlement in 15 cm, what is the reliability against...
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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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