The method of least squares in MatlabGiven data setxk00.10.20.30.40.50.60.70.80.91yk0.78290.80520.57530.52010.37830.29230.16950.08420.04150.0090Use Matlab functionpolyfitto find respectively the first, second, fourth and eighthorder polynomials that best fit the data, using the method of least squares. You shouldalso plot your polynomials, together with the data set.What to hand in:The script file, the plots, and your comments.

a) 33.33%)

b) 135 minutes

c) 8.66 min

d) 50%

Step-by-step explanation:

a) the probability for a uniform distribution is

P(b<X<a) = (a-b)/(c-d) , where c and d are the maximum and minimum values

therefore the probability that the flight is more than 140 minutes ( and less than 150 since it is the maximum value)

P(140<X<150) = (a-b)/(c-d) = (150-140)/(150-120) = 10/30 = 1/3 (33.33%)

b) the mean (expected value) for a uniform probability distribution is

E(X) = (c+d)/2 = (120+150)/2 = 135 minutes

c)  the standard deviation for a uniform probability distribution is

σ²(X)= (c-d)²/12 = (150-120)²/12 = 75 min²

σ = √75 min² = 8.66 min

b) following the same procedure as in a)

P(120<X<135) = (a-b)/(c-d) = (135-120)/(150-120) = 15/30 = 1/2 (50%)