Consider a bridge with two columns. As the foundation system settles, settlments of the two columns are denoted, respectively, byS

1

S

1

andS

2

S

2

. LetD

D

denote the differential settlement, expressed asD

=

|

S

1

S

2

|

.

D

=

|

S

1

S

2

|

.

Assume thatS

1

S

1

has a mean and variance of

1

1

,

2

1

1

2

, whileS

2

S

2

has a mean and variance of

2

2

and

2

2

2

2

. Also assume that they are correlated with a correlation coefficient denoted by

.

1. What is the difference between the first order and the second order estimates of the mean ofD
2. D
3. ?
4. Give your best estimate of the variance ofD
5. D
6. ?