(a) The following table presents the effective normal stress (in kN/m2) and the shear stress at failure (in kN/m2) obtained from direct shear tests on specimens of a sand compacted to in-situ density for the determination of the shear strength parameters c' and '.
Effective normal Stress (kN/m2) 50 100 150 200 250 300
Shear stress at failure (kN/m2) 44 91 129 176 220 268
(i) Compute the least-squares regression line for predicting shear stress at failure from normal stress.
(4 marks)
(ii) Compute the coefficient of determination.
(2 marks)
(iii)Compute the residual for each point and the sum of squares for the error (SSE).
(2 marks)
(iv) Predict the shear stress at failure if the effective normal stress is 160kN/m2. (1 mark)
Hints:
S
Bay-Bxre=y-y; for (i), (ii) & (iii).
وگیری
(b) Fatal traffic accidents were recorded at a given station over a period of 50 years. During this period, the frequencies of fatal accidents observed are as follows: 13 years with zero accident; 15 years with one accident; 12 years with two accidents; 6 years with three accidents; 4 years with four accidents
Assume that the occurrence of fatal accidents in a year may be modeled with the Poisson process. The probability mass function is
(vt)x
P(x)
-e-vt x = 0,1,2,...
x!
(i) Estimate the parameter v of the Poisson distribution by the method of moments.
Hint: E(X) = μ = vt
(2 marks)
(ii) Perform the chi-square goodness-of-fit test for the Poisson distribution at the 5% significance level. [Use k=5 intervals of 0, 1, 2, 3 & 24 no. of accidents per year]
(9 marks)