=========================preview======================
(CIVL181)[2010](s)midterm~wmma^_10062.pdf
Back to CIVL181 Login to download
======================================================
1)

X and Y are independent random variables, their PDFs are:








Let Z = X + Y, find

a) FZ(z) when z < 0 (2%)

b) FZ(z) when z > 3 (3%)

c) FZ(z) when 0 z 1 (10%)


d) FZ(z) when 2 z 3 (10%)




2)

A student got his score of 50 in the midterm. If the score distribution of the class follows either normal or log-normal distributions and both with mean and SD of 80 and 20, under what score distribution the student actually performed worse in the midterm? (10 %)



3)

An antenna is designed against wind load. During a wind storm, the maximum wind-induced pressure on the antenna, P, is computed as:




Where C = drag coefficient; R = air mass density in slugs/ft3; V = maximum wind speed in ft/sec; and P = pressure in lb/ft2. C, R, V are statistically independent and following lognormal distributions with respective mean and coefficient of variations











Find:

a) What is the probability that the maximum wind pressure will exceed 30 lb/ft2 ? (10%)

b) The actual wind resistance capacity of the antenna is also a lognormal random variable with a mean of 90 and coefficient of variation of 0.15. What is the probability of failure of the antenna? (10%)

c) following b), if the failure of antenna follows a Poisson distribution and it is reported that the failure occurs once in five year. Please find what is the probability of the failure of the antenna in 25 years ? (10%)

d) following c), suppose five antennas were built and installed in a given region. What is the probability at least two of five antennas will not fail in 25 years? Assume that failures between antennas are statistically independent. (10%)



4)

If X follows the uniform distribution between a and b, find:

1)
Median (1 %)


2)
Variance (10 %)


3)
skewness (2 %)


4)
75th percentile (2%)





5)

Show
(10%)