**Expected value of a continuous random variable :**

Expected value or Mathematical Expectation or Expectation of a random variable may be defined as the sum of products of the different values taken by the random variable and the corresponding probabilities.

For example, if a continuous random variable takes all real values between 0 and 10, expected value of the random variable is nothing but the most probable value among all the real values between 0 and 10.

That is, the value which has more chance to occur.

Let "x" be a continuous random variable which is defined in the interval (-∞ , +∞) with probability density function f(x).

Then, the expected value is given by

Expected value of x² is given by

**Note :**

Expected value is also called as mean

1. Expectation of a constant k is k

That is,

E(k) = k for any constant k

2. Expectation of sum of two random variables is the sum of their expectations.

That is,

E(x + y) = E(x) + E(y) for any two random variables x and y.

3. Expectation of the product of a constant and a random variable is the product of the constant and the expectation of the random variable.

That is,

E(kx) = k.E(x) for any constant k

4. Expectation of the product of two random variables is the product of the expectation of the two random variables, provided the two variables are independent.

That is,

E(xy) = E(x).E(y)

Whenever x and y are independent.

**Example 1 :**

In a continuous distribution, the probability density function of x is

Find the expected value of x.

**Solution :**

Expected value of "x" is given by

Therefore, the expected value of "x" is 1

**Example 2 :**

In a continuous distribution, the probability density function of x is

Find the expected value of x.

**Solution :**

Expected value of "x" is given by

Therefore, the expected value of "x" is 1/3

After having gone through the stuff given above, we hope that the students would have understood "Expectation of a continuous random variable".

Apart from the stuff given above, if you want to know more about "Expectation of a continuous random variable", please click here

Apart from "Expectation of a continuous random variable", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**