Question

.4 In a simple frame structure such as the one shown in Figure 3.1, the total horizontal displacement of top storey Y is the sum of the displacements of individual storeys Xl and X2. Assume that Xi and X2 are independent and letmxmx and oi, be their respective means and variances. (a) Find the mean and variance of Y (b) Find the correlation coefficient between X2 and 1Y Figure 3.1 Frame structure, for Problem 3.5

Answer 1

3. 4 2 tHere and 2 ave independent a The mean of y is N't下2)

he vaiance ot Y is Var (Y): Var (x, .) Var () + Var(x2) 2 2 bo> Fore any an dom X2 CAVXx) x. Van( x) The covwelahion co efficient behween X2 and y is

2. 2 2. 2 2