## What are the properties of mathematical expectation?

E(aX+b)=aE(X)+b, where, a and b are constants. The mathematical expectation of a linear combination of the random variables and constant is equal to the sum of the product of ‘n’ constant and the mathematical expectation of the ‘n’ number of variables.

**What are the properties of conditional expectation?**

In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take “on average” over an arbitrarily large number of occurrences – given that a certain set of “conditions” is known to occur.

**Can you multiply expectations?**

Multiplying a random variable by any constant simply multiplies the expectation by the same constant, and adding a constant just shifts the expectation: E[kX+c] = k∙E[X]+c . For any event A, the conditional expectation of X given A is defined as E[X|A] = Σx x ∙ Pr(X=x | A) .

### What is the multiplication theorem of expectation?

The second property is that of the multiplication theorem. This property of the mathematical expectation states that if there is an X and Y, then the product of those two random variables are equal to the product of the mathematical expectation of the individual random variables.

**How do you solve mathematical expectations?**

The mathematical expectation of a random variable X is also known as the mean value of X. It is generally represented by the symbol μ; that is, μ = E(X). Thus E(X − μ) = 0. Considering a constant c instead of the mean μ, the expected value of X − c [that is, E(X − c)] is termed the firstmoment of X taken about c.

**What is conditional mean in statistics?**

Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening.

#### How do you calculate conditional mean?

The conditional expectation (also called the conditional mean or conditional expected value) is simply the mean, calculated after a set of prior conditions has happened….Step 2: Divide each value in the X = 1 column by the total from Step 1:

- 0.03 / 0.49 = 0.061.
- 0.15 / 0.49 = 0.306.
- 0.15 / 0.49 = 0.306.
- 0.16 / 0.49 = 0.327.

**How do you calculate expected frequency?**

Expected Frequency = (Row Total * Column Total)/N. The top number in each cell of the table is the observed frequency and the bottom number is the expected frequency.

**How do you calculate variance and expectation?**

The expected value µ = E(X) is a measure of location or central tendency. The standard deviation σ is a measure of the spread or scale. The variance σ2 = Var(X) is the square of the standard deviation.