# Expected Value tutorial

**Expected value tutorial:** Welcome to Data science tutorials from Prwatech, In this one can learn about expected value in data science and how to calculate it with examples. Before we proceed, we recommend you to go through the previous blog in this series on how to calculate the probability density function in data science.

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## What is the Expected Value?

Expected Value in Data Science of a Random Variable is the theoretical mean of the random variable.

It is exactly what you might think it means intuitively: the return you can expect for some kind of action, like how many questions you might get right if you guess on a multiple-choice test.

### Why we need the Expected Value?

Suppose if you take 200 questions multiple-choice test with A, B, C, D as the answers, and you guess all “D”, then you can expect to get 25% right

The **calculation** behind this kind of expected value is:

The probability (P) of getting a question right if you guess: .25

The number of questions on the test (n)*: 20

**P x n = 0.25 x 200 = 50. ****This is as Expect Value.**

## Expected Value Formula

## Expected Value Example

- A stack of cards contains one card labeled with 1, two cards labeled with 2, three cards labeled with 3, and four cards labeled with 4. If the stack is shuffled and a card is drawn, what is the expected value of the card drawn?

**Solution:**

Let X be the random variable that represents the value of the card drawn. Then

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