Basics of ML & AL Week 2 Challenge

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

sol: See the Document in pdf

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

It is true that a simple mean is sufficient enough for having an idea about the data by computing with it's formula(sum of all observations/number of observations)

Assume we have 4 events possibly to occur namely A, B, and C. So we are given their number of occurrence in definite numbers say, A happens for 4 times, B happens for 8 times and so on.
For this scenario simple mean itself is enough. But what if instead of their number of occurrences their probability is given? For example, the possibility of A to occur is 0.48, and the possibility of B to occur is 0.31, and c is 0.21.
This would give us a point, where we need to consider the weight of events as given in the example above the probability of A, is more than B and C. That means when we correlate this with its occurrence we can infer that the mean or the ideal possibility of the event to occur would be closest of that of A and farther
from C(Holding the least probability) imagine having more random variables and complex probability values. That is when the significance of the expected mean value overcomes the simple mean value. As explained in the previous question instead of summing the probability we should consider the weight of each event before averaging them.

The expected value of a random variable is the weighted average of all possible values of the variable. The weight here means the probability of the random variable taking a specific value.

Note: The sum of the probabilities should always be 1.

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

Skewness is the measure of the asymmetry of an ideally symmetric probability distribution and is given by the third standardized moment

In simple words, skewness is the measure of how much the probability distribution of a random variable deviates from the normal distribution.

One cannot determine whether having skewness is good or bad. Because different types of skewness depicts the data according to the domain of its application.

The probability distribution with its tail on the right side is a positively skewed distribution and the one with its tail on the left side is a negatively skewed distribution.

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

d)P(X=720)

To evaluate the probability value for continuous normal distribution we calculate the z-score with the given mean and standard variation for each of the data points given by the formula

Z-score =(X-mean)/standard deviation

a)P(X<711)
z-score of this would be=(711-680)/31=1
Hence it is one standard deviation away from the mean in a positive x-axis
In the z-table, the probability value for z=+1 is 0.8413 which is 84.13%

b)P(X>740)

z-score would be =(740-680)/31=1.93
Hence it is 1.9 times the standard deviation away from the mean in a positive x-axis
In z-table, the probability value for z=+1.93 is 0.9732 which is 97.32%

But asked for probability greater than 740 so subtract from 1
1-0.9732=0.0268 or 2.68%

c)P(600

In this case, we need to find the value of probability at x<720 and x<600 and subtract noh values
When x=720, z=1.29 and pobability value is 0.9015
When x=600, z=-2.58 and probability value is 0.00494
probability value =0.9015-0.00494=0.89656 or 89.656%

d)P(X=720)

P(Z=1.29)=P(1.29<Z<1.29)
Since our primary aim is to compute the area of the curve whether it is to left or right depends on its position and if it is greater or lesser
Hence being a single line the area enclosed by it is zero
P(Z=1.29)=P(Z<1.29)-P(Z<1.29)
P(Z=1.29)=0.9032-0.9032
P(Z=1.29)=0

5)Explain the curve on the right side

Here, the mean of this observation data is always 0 and the standard deviation is 1
It gives us the percentage of data falling under every 1,2, and 3 standard deviations from the mean value
In this figure 68.2% of the data falls from z value -1 to +1, 95.4% from -2 to +2 and 99.6% from -3 to +3

An example would be marks obtained in a test. It can be observed that people who scored centum and people who scored a zero would be very less. More student's marks would be around the average class mark