Basics of ML & AL Week 2 Challenge

1. Calculate all for business movements using pen and paper for the below data set

X(Random variable= Number of toys )	P(x)= Probability of selling x toys in a day
0	0.35
1	0.25
2	0.15
3	0.15
4	0.10

Business moments	Formula	Value
First business moment-Mean	`μ=∑▒〖(x_i*p(x))〗`	`μ=1.4`
Second Business moment-Variance	`σ^2=∑▒〖(x_i-μ)〗^2 *p(x)`	`σ^2=1.84`
Third Business moment-Skewness	`Sk=∑▒〖(〖(x_i-μ)/σ)〗^3*p(x)〗`	`sk=0.57`
Forth Business moment-Kurtosis	`ku=∑▒〖(〖(x_i-μ)/σ)〗^4*p(x)-3〗`	`ku=-0.98`

What is the significance of expected value when sample mean (sum of all observation/ number of observations) are already in place?

Sample mean is defined as the sum of individual observation divided by the number of observations

`Mean is given by (∑▒x_i )/n`

Expected value: probability of an event multiplied by the amount of times the event happens`p(x)*n`

Expected value gives more clarity of an event than mean for example if we toss a coin ten times the probability of getting head or tail is 0.5 the total number of trial =10 so we can expect out of 10 trials 5 trails we can expect head

Having skewness in the curve considered to be bad in the analysis?

Having skewness in the curve is not considered to be bad in the analysis. It depends on types of data to be analyzed.

Skewness is a measure of how much the probability distribution of a random variable deviates from the normal distribution

Evaluate the probabilities for continues normal distribution with given mean =680 and standard deviation =31

To evaluate the probabilities for continues and normal distribution we use ‘z- formula’ and ‘z-table’

`z=(x-μ)/σ`

Explain the curve

It gives us the percentage of data falling under every 1,2,3 standard deviation from mean value. In the figure 68 % data falls from z value -1 to +1 , 95% from -2 to +2 and 99.6% from -3 to 3

Explain kurtosis

Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution.

There are three types of kurtosis: mesokurtic, leptokurtic, and platykurtic.

• Mesokurtic: Distributions that are moderate in breadth and curves with a medium peaked height.
• Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails)

• Platykurtic: Fewer values in the tails and fewer values close to the mean (i.e. the curve has a flat peak and has more dispersed scores with lighter tails).