Basics of ML & AL Week 2 Challenge

1)First Business moment = mean = 1.40

second business moment = variance = 1.6655

third business moment = skewness = 0.11379 (approx.)

fourth business moment = kurtosis = 0.86602(approx.)

2) the expected value is a concept used in probability theory and involves random variables and probabilities, while the simple mean is a descriptive statistic used to summarize the central tendency of observed data.

3) it is neither considered wrong nor right as it totally depends on the situation or distribution we are solving for.

4)

a.

x < 711

711-680/31= 1

after finding z value from 0 to 1 and summing the left 50 %

34% + 50%= 84%

b.

x>740

740-680/31= 1.93

= .4732 = 47%

after finding z value from 0 to 1.93 and summing the left 50 %

47+50=97%

1-97= 3%

c.

p(680<x>740)

z(600) = 600-680/31= 2.58

z(740)= 740-680/31= 1.29

for 2.58 = .4946

for 1.29 = .4015

.4946-.4015= .0931= 9.31 %

d.

0 as it is a continuous normal distributio and probability is calculated on the basis of area under the point and if x = 780 then there is zero area under it hence 0 % probability.

5)

it is a probability graph in which we find the z values for different sigma values.

vertical side denotes the frequency of the event where as horizontal side represents random variables sigma values.

the value between 1sigama and -1 sigmaa is approx 68%

whereas between -2 and 2 is 95% and so on

and the type of the graph is kurtosis