Basics of ML & AL Week 2 Challenge
The first question solution is in the excel file attached below.
2) Expected value : It is termed as the average value or mean that is expected to obtained when multipled by the values of the x with their probablity measures. This value is expected to be obtained when we conduct an experiment whose value are represented by random variable. In probablity theory the expected value refers to the value of a random variable that is expected to obtain when you repeat the random variable process infinite times and take an average of the obtained values. The expected values is also termed as weighted average of all possible values. The weights used in computing the average are the probabilities obtained for discrete random variables or the values of a probability density function obtained for continuous random variables.
3) Skewness is a measure of how the probability distribution of data of a random variable deviates from the normal distribution. A normal distribution is distributed without any skewness. So with skewness involved, we have positive skewness and negative skewness. So having a skewness is considered anything bad. Hopefully not since when we have presented skewness we are working on an asymmetry and the tail is distinguished with the side on which the tail of probability distribution lies. So linear models work on assumption that the distribution is independent of variable and the target variable are similar. So having skewness of data helps in creating better linear models. The skewness also tells us about the direction but does not tell about the number of outliers.
4) The probability of distribution having P(x<711) is 0.8413 since it is one deviation on the right side of the curve. so total percentage of probability from zero to one deviation on the right is 0.8413.
The probability distribution with P(x> 740) is 0.9738
The probability distribution between P(600<x<720) is 0.8966
The probability distribution for P(x = 720) is 0.9015
5) The normal distribution curve is a continuous probability distribution that is symmetrical on both sides of a mean. The area under this normal distribution represents probability and the total area of the curve sums to one.
Most of the probability is calculated based on the mean that is center of the curve. It is often called a bell curve because it looks like a bell. The empirical rule of a normal distribution curve is based on three-sigma rule which is 68-95-99.7 rule.
The 68% data falls within one deviation curve from the mean that is +1 and -1 deviation from the mean. The 95% probability falls under two standard deviations from the mean and the 99.7% falls under three deviations from the mean.