Basics of ML & AL Week 2 Challenge

1) Soluton attached in PDF for first business moment and in excel sheet for other business moments

2) Expected value is used to calculate the mean of probability distribution.Expected value is the average outcome if we repeat the random process for a number of times.

Mean can be used when there is uniform probability. In case of non uniform probability distribution weighted average has to be considered hence expected value becomes significant.

3) Having skewness is neither good or bad. Its a measure of distribution and depends on the anlysis.

But having skewness can make the analysis difficult because we cannot try different models which are not robust to skewness.To overcome this difficulty we can try to transform the skewed data to close enough normal distribution.

4) `Z = (X-mu)/sigma`

a)

Z score of 711 = `(711 - 680)/31=1`

From Z score table P(x < 711) = 0.84134

b)

Z score of 740 = `(740 - 680)/31`= 1.93

From Z score table P(x < 740) = 0.97320

P (X > 740) = 0.0268

c)

P(600<X<720)

Z score of 600 = `(600 - 680)/31`= -2.58`

Z score of 720 = `(720 - 680)/31`= 1.29`

P(600<X<720) = P(X<720) - P(X<600)

From Z score table P(x < 600) = 0.00494

From Z score table P(x < 720) = 0.90147

P(600<X<720) = 0.90147 - 0.00494 = 0.89653

d) P (X = 720) = 0

Because X=720 will be a straight line and area under a straight line is zero

5) The curve is a standard normal distribution curve plotted based on the Z - score. The curve will be symmetric about its mean.

34.1% of the population is within one standard deviation of the mean on each side. Hence, nearly 68% of the population is within one standard deviation away on the either side of mean

Similarly another 13.6% of the population is between one and two standard deviations.

2.1% of the population is between two and three standard deviations.

0.1% of the population is between three and four standard deviations.