Basics of ML & AL Week 2 Challenge

1)Calculate all 4 business moments using pen and paper for the below data set?

Answer is mentioned as in below attachment Image 01.

2)What is the significance of expected value when simple mean (Sum of all observations/number of observations) is already in place

For very large number of population/ elements in a data set, which are not having "Equiprobable" outcomes, at that point of time so called Expected Value is best suitable for representing the outcome of occurance of an event whose possible outcomes are represented by random variable x.

Regardless if outcomes are equiprobable then both mean and expected value of that data set are same. For eg. tossing a die and expecting what could be outcome : Here both mean and expected value are same as probability of occurance of every single number is (1/6).

In general regardless of equiprobable outcomes, mean and expected value differes from formula only. Like if we have the frequency of occurance of outcomes of the data then multipling them with variables, summing up and then dividing with total number of frequency gives us sampke mean.

While if we have probability of occurance of variables in data set of ramdom variables, then summation of multiplication of variables with their probability occurance gives us expected value of population.

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

Skewness is basically the measurement of whether the data set is symmetric (like normal distribution) or it lacks the same. Almost all real world examples are having Skewed data set ( both positive and negative ) but if there is too much skewness in data set then statistical model of data set doesn't work effectively. In such analysis, tail region of skewed data det act like outliner which is adversely affecting the model's performance, especially of regression based model. So in most cases the skewness is preferred to be removed by certain models(like tree model).

Generally having positive skewness is considered to be good depending on whether mean is positive or negative. While negative skewness is generally considered as bad, as it highlights the risk of left tail events which is referred to as “black swan events.”

Skewness tells us about which portion of curve probability is biased and so accordingly their probability distribution varies from normal distribution curve.

4)Evaluate the probabilities for continuous normal distribution with given mean = 680 and standard deviation = 31

a)P(X<711)

b)P(X>740)

c)P(600<X<720)

d)P(X=720)

It is basically a continuous normal distribution. See below attachment IMG_02, IMG_03.

5)Explain the curve on the right side

Basically this is a normal distribution curve of the random variable representing the deviation of variables from mean in form of percentage as wrote on curve. On the either side of mean the probabilities are equally distributed.

The right hand side of curve basically represents the probabilities of occurance of outcomes which are havin numerical value greater that mean of dataset. Let us take the dark blue section right to mean. Ot represents that of 100 % dataset values, only 34.1% of the values of the data set lies between mean and 1 standard deviation (on either side) i.e. total 68.2% values falls in 1 standard deviation. It tells us about the possibility of the values from data set having how much deviation from mean or can say how many values of data set are in between mean and 1 standard deviation. For large popution this information is worth.

Similarly between mean and 2 standard deviations probability 34.1%+13.6% lies on either side, i.e. total 95.4% values of the 100% data set values falls under 2 standard deviation from mean.