Basics of ML & AL Week 2 Challenge

2. Mean and Expected value

Mean(µ) indicates the average value of the outcome when probability of all outcomes in that sample space is equal. Expected value(E(X)) is the weighted average calculated by multiplying the number of occurrences of outcome and probability of outcome.

Let x1, x2, x3…,xn in sample space and p1,p2,p3,…pn are its probability.

Mean = x1+x2+x3+…+xn/n

Expected value = p1.x1+p2.x2+p3.x3+…..+pn.xn

Mean is the special case of expected value having probabilities of all outcomes are equal.

3. Skewness

Skewness, in statistics, describes the measure of asymmetry in the data. There are several ways to determine skewness. Pearson’s first and second coefficients are the most widely used. Pearson’s first coefficient is also called Pearson’s mean coefficient and second is also called Pearson’s median coefficient.

Skewness is very helpful for investors to better judge the likelihood of events in the tail of the probability distribution. With this, they can determine their investments accordingly to stay in the market for a long time

However, skewness, in data, is considered to be bad for analysis. Because, all the statistical methods, that we are using to describe the data, are assuming that the distribution is normal i.e. without skewness. When these methods are used on skewed data, it will end up in a misleading result. Therefore, to get better result, we have to use advanced mathematical techniques and quantile regression which are complex in nature.

4.

Given data :

Mean (µ) = 680

S.D (σ) = 31

• P(X< 711) = P (-∞ < X < 0) + P(0 < X < 711)

For X = 711, Z = 1.

P(-∞ < X < 711) = P (-∞ < Z < 1)

= 0.8413

• P(X>740) = 1 – P(X<=740)

For X = 740, Z = 1.93

1 – P(X<=740) = 1- P(Z<=1.93)

= 1 – 0.9732

= 0.0268

• P(X = 720) = P(719<X<721)

For X = 719, Z = 1.25

For X = 721, Z = 1.32

P(719<X<721) = P(-∞ < Z < 1.32) – P(-∞ < Z < 1.25)

= 0.9066 – 0.8944

= 0.0122

5. The curve represents a normal distribution. This is the curve that belongs to a famous technique called six-sigma. Six sigma is a quality control technique to evaluate each process using available data and control the problem that is occurring. If an organization uses six sigma, it can produce defect free product in 99.7% of the time. Six Sigma points to the fact that, mathematically, it would take a six-standard-deviation event from the mean for an error to happen

68.2% of product lies within ±1σ

95.4% of product lies within ±2σ

99.7% of product lies within ±3σ

References:

1. https://www.investopedia.com/terms/s/skewness.asp#:~:text=Investors%20commonly%20use%20standard%20deviation,is%20due%20to%20skewness%20risk.
2. https://www.statisticshowto.com/skewness/#:~:text=Calculation.,an%20alternative%20Pearson%20Mode%20Skewness.
3. https://www.statisticshowto.com/probability-and-statistics/skewed-distribution/
4. Standard 12, Mathematics book – Volume – II
5. https://www.sciencedirect.com/topics/mathematics/skewed-distribution