Probabilities Review

Given:
Totals = {20: 16576, 30: 16619, 40: 16632, 50: 16805, 60: 16664, 70: 16704}
Purchases = {20: 3392, 30: 4974, 40: 6670, 50: 8319, 60: 9944, 70: 11713}


totalPurchases = 45012
Sample size (total no. of people) = 100000.0


Purchases[30] : This means the number of persons at age 30 who did a purchase.
Totals[30] : This means the total number of persons at age 30.


- P(Age)
The probability of 30's persons(P(30)): totals[30]/100,000

-P(Purchase)
And P(Purchase) is the overall probability of buying something, regardless of your age:
P(Purchase) = float(totalPurchases) / 100000.0

- P(Purchase|Age) : (نسبة الشراء في هذه الفئة العمرية)
The probability of someone in their 30's buying something
P(Purchase|30) = total_persons_of_30s_did_purchase/total_Persons_Of_Age_30 = purchases[30]/totals[30]

-P(Purchase, Age) :  [comma means both and when we say both we mean according to total population] (نسبة شراء هذه الفئة العمرية بالنسبة للمجتمع ككل)
The probability of both being in your 30's and buying something, out of the total population
P(30's, Purchase) = purchases[30] / 100000.0

- If Purchase and Age were independent:
  • P(Purchase | Age) ≈ P(Purchase) (احتمال الشراء لفئة عمرية معينة هو نفس احتمال الشراء لجميع الفئات العمرية حيث لا توجد علاقة بين العمر والشراء)
  • P(Purchase, Age) ≈ P(Purchase) * P(Age) (احتمال\نسبة الشراء لفئة عمرية يساوي نسبة أو احتمال هذه الفئة العمرية مضروب في النسبة العامة\أو الاحتمال العام لجميع عمليات الشراء)
- If Purchase and Age were dependent:
  • P(Purchase | Age) =   P(Purchase, Age) ÷ P(Age)    (Proved Theory)
Prove:
P(Purchase, Age) / P(Age) = Purchases[30]/100,000 ÷ Totals[30]/100,000
  = Purchases[30]/Totals[30]
  = P(Purchase|Age)

Comments

Post a Comment

Popular posts from this blog

Maxpooling vs minpooling vs average pooling

Image
Pooling is performed in neural networks to reduce variance and computation complexity. Many times, beginners blindly use a pooling method without knowing the reason for using it. Here is a comparison of three basic pooling methods that are widely used. The three types of pooling operations are: Max pooling: The maximum pixel value of the batch is selected. Min pooling: The minimum pixel value of the batch is selected. Average pooling: The average value of all the pixels in the batch is selected. The batch here means a group of pixels of size equal to the filter size which is decided based on the size of the image. In the following example, a filter of 9x9 is chosen. The output of the pooling method varies with the varying value of the filter size. The operations are illustrated through the following figures. Average, Max and Min pooling of size 9x9 applied on an image We cannot say that a particular pooling method is better over others generally. The choice of pooling operation is made...
Read more

Percentiles, Deciles, and Quartiles

Image
Percentiles Percentile: the value below which a percentage of data falls. Example: You are the fourth tallest person in a group of 20 80% of people are shorter than you: That means you are at the  80th percentile . If your height is 1.85m then "1.85m" is the 80th percentile height in that group. In Order Have the data  in order , so you know which values are above and below. To calculate percentiles of height: have the data in height order (sorted by height). To calculate percentiles of age: have the data in age order. And so on. Grouped Data When the data is grouped: Add up all percentages  below  the score, plus  half  the percentage  at  the score. Example: You Score a B! In the test 12% got D, 50% got C, 30% got B and 8% got A You got a B, so add up all the 12% that got D, all the 50% that got C, half of the 30% that got B, for a total percentile of 12% + 50% + 15% =  77% In other words you...
Read more

Data Warehouse Vs Data Mart

Image
What is Data Warehouse? A Data Warehouse collects and manages data from varied sources to provide meaningful business insights. It is a collection of data that is separate from the operational systems and supports the decision making of the company. In Data Warehouse, data is stored from a historical perspective. The data in the warehouse is extracted from multiple functional units. It is checked, cleansed and then integrated with the Data warehouse system. Data warehouse used a very fast computer system having large storage capacity. This tool can answer any complex queries relating to data. What is Data Mart? A data mart is a simple form of a Data Warehouse. It is focused on a single subject. Data Mart draws data from only a few sources. These sources may be central Data warehouse, internal operational systems, or external data sources. A Data Mart is an index and extraction system. It is an important subset of a data warehouse. It is subject-oriented, and it is desig...
Read more