Problem 1: Lifetime of a VLSI chips manufactured by company X is a normal distribution with μ = 5 * 106 hours and σ = 5 * 105 hours. Your company needs a batch that has at least 95% of the chips with life time greater than 4* 106 hours.
Will you close this deal?
Problem 2: A battery manufacturer claims its product is normally distributed with a life time of average 3 years and a standard deviation of 0.5 years. What is the probability that a battery you purchased lasts more than 2 years?
Problem 3.
a. Fibonacci sequence is found everywhere in nature. Do a google search and read about the presence of 'golden ratio' and the sequence in engineering designs. Write about one example that interests you.
b. Write a Matlab code to generate the Fibonacci sequence to generate the first 20 terms.
c. Plot the golden ratio for the sequence and notice how the ratio approaches a constant.
Problem 4. Write a code to carry out 100 iterations on the recurrence relation
Xn+1 = 4Xn(1 - Xn)
i. Given initial condition X(0) = 0.2
ii. Given initial condition X(0) = 0.2001
iii. List the final 10 iterations in each case.