1. If a random variable has the log-normal distribution with =-1 and probability
ID: 3331704 • Letter: 1
Question
1. If a random variable has the log-normal distribution with =-1 and probability that the random variable will take on a value (a) between 3.0 an 12; -B= 7.32, find the 2. The daily consumption of water in millions of gallons in a certain city can be treiat variable having a gamma distribution with -4 and -3. If the water to capacity of 12 million gallons find (a) the probability that this water supply will be inadequate on any given day (b) the probability that this water supply will be adequate on any given day if the da changed to 13, 14, 15, 16, and 17 million gallons. tower of this city has a daily You must show the Excel/Matlab programming statements for your answers. be looked upon as a 3. Suppose the proportion of defective screws made by a machine tool may random variable having the beta distribution with =2 and =3. (a) Find the probability that the screws made by this machine tool wi defective screws contain 25% or more complta computer programming using Matlab/Excel to find the probability that the screws made by this machine tool will co , 25% defective screws ntain more than 10%, 1 1 % i 2%, l 3%, 4. Consider the random variable X, the time to failure of a computer chip ( in minutes), has a following Weibull density or = 0 elsewhere. with parameter =1/5 and -1/4 (a) How long can such a computer chip be expected to last? (b) what is the probability that such a chip will fail in less than 10 hours? (c) complete a computer program to find the probability that such a chip will not fail in 1, 2, 3, 4, 5,6, 7,8,9, 10 hours.Explanation / Answer
1)
a) Excel formula:
=LOGNORM.DIST(10,1,7.32,TRUE)-LOGNORM.DIST(3,1,7.32,TRUE)
Ans: 0.0652
b) Excel Formula :
=LOGNORM.DIST(12,1,7.32,TRUE)
Ans: 0.5804 (upto 4 decimal places ) (As per given by Excel)
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