Basics of ML & AL Week 2 Challenge

1)Calculate all 4 business moments using pen and paper for the below data set?
x p(x) x*p(x) X-mean (X-mean)2*x ((X-mean)/variance))^3 ((X-mean)/variance))^4
0 0.35 0 -1.4 0 -0.012918411373136 0.003031182931448
1 0.25 0.25 -0.4 0.16 -0.00030130405535 2.01994697639187E-05
2 0.15 0.3 0.6 0.72 0.001016901186807 0.00010225981568
3 0.15 0.45 1.6 7.68 0.019283459542407 0.005171064259563
4 0.1 0.4 2.6 27.04 0.082745626200524 0.036057315995455
mean 1.4 standard deviation 35.6 0.089826271501251 0.04438202247191
variance 5.96657355607052
Skewness 0.089826271501251
kurtosis 0.04438202247191

2.What is the significance of expected value when simple mean (Sum of all observations/number of observations) is already
in place
Expected mean is weighted mean for random variables in a probability distribution.
Simple mean is average for a given sample.

3.Having skewness in the curve considered to be bad in the analysis?
Having a skewness is disoration of the curve from the normal distribution.
It not either good or bad to have a skewness in the curve.

4.Evaluate the probabilities for continuous normal distribution with given mean = 680 and standard deviation = 31
z =(x-mean)/standard deviation

a.P(X<711)
z = 1
84.12%

b.P(X>740)
z = 1.9 = 2
2.27%

c.P(600<x<720)
83.99%

d.P(X=720)
0%

5.5)Explain the curve on the right side
The right side of the normal distribution represents the high chance of finding better performer or best scoring student or higher paid employees.