here error in one segment follow uniform distribution with parameter a=-10 and b=10
hence mean =(a+b)/2 =0
and std deviation =(b-a)/sqrt(12)=5.7735
for n=100; railroad segments ; expected deviation from true length =100*0 =0
and standard deviation of total error =5.7735*sqrt(100)=57.735
therefore from normal approximation;
P(overall estimated length will be within 100 milimeters of true length)=P(-100<X<100)
=P((-100-0)/57.735<Z<(100-0)/57.735)=P(-1.73<Z<1.73)=0.9582-0.0418 =0.9164
2. (15pts) The lengths of 100 railroad tracks segments are measured independently using the same device....
The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4. (a) Write down the distribution (pdf) of the daily rainfall in Dublin. (b) Use Markov’s inequality to upper bound the probability that the observed rainfall in a given day is larger than 3 mm, and compare the value to its true counterpart. (c) Consider the overall rainfall in 365 days, and use mgfs and their properties to...