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)	p*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 is 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)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.