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also a lognormal variate.
n Let, Z X i where, X i ’s are statistically independent lognormal 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 lognormal 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 lognormal 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.
 Spring '13
 Dr.RajibMaity
 Civil Engineering

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