1.) Consider two chains R and S, each having 3 and 6 links respectively. Each link's resisting strength is normally distributed with a mean of 60,000 psi and standard deviation of 5,000 psi.
Determine which chain is generally weaker. Also, plot the probability distribution functions of their resisting strengths.
2.) The annual maximum stage height in a river channel is modeled by a Type I asymptotic distribution of the largest value, with a mean value of 30 ft and a coefficient of variation of 10%.
The stage height at which flooding is known to occur is 40 ft. What is the probability that the annual maximum stage height will exceed this level?
3.) A steel cable consists of 8 high-strength steel strands. The strength of each strand can be modelled by a lognormal RV with a mean value of 50 kips and a coefficient of variation of 10%. What is the probability that the weakest strand will have strength less than 40 kips? Also:
a. Calculate this probability if the cable consists of 16 strands.
b. Of 32 strands.
c. Of 64 strands.