## How do you calculate conditional expectation continuous?

Conditional expectation and variance are similarly defined. Given Y=y, we need to replace fX(x) by fX|Y(x|y) in the formulas for expectation: For two jointly continuous random variables X and Y, we have: Expected value of X given Y=y: E[X|Y=y]=∫∞−∞xfX|Y(x|y)dx.

## Can you give 5 examples of continuous random variables?

In general, quantities such as pressure, height, mass, weight, density, volume, temperature, and distance are examples of continuous random variables.

What is the expectation of a continuous random variable?

The formula for the expected value of a continuous random variable is the continuous analog of the expected value of a discrete random variable, where instead of summing over all possible values we integrate (recall Sections 3.6 & 3.7).

### Which is an example of a continuous random variable?

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile. A continuous random variable is not defined at specific values.

### What do you mean by 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.

How do you find the conditional distribution of a random variable?

Conditional Distributions of Discrete Random Variables. P(A | B)=P(A∩B)P(B). We use this same concept for events to define conditional probabilities for random variables.

#### What are three examples of continuous variables?

Therefore, at a macroscopic level, the mass, temperature, energy, speed, length, and so on are all examples of continuous variables.

#### What are 5 examples of continuous data?

Examples of continuous data:

• The amount of time required to complete a project.
• The height of children.
• The amount of time it takes to sell shoes.
• The amount of rain, in inches, that falls in a storm.
• The square footage of a two-bedroom house.
• The weight of a truck.
• The speed of cars.
• Time to wake up.

How do you find the expected value of a random variable?

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).

## How do you find the expected expectation in math?

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.

## Which is not an example of continuous random variable?

Height is not an example of a continuous variable.

Why is conditional expectation important?

We use conditional expectation because we expect there to be a relationship between a predictor variable and the response variable, such that we want our predictions to be made in the context of a specific value of the predictor(s).

### Is conditional expectation unique?

Uniqueness: If it exists, the conditional expectation is unique.

### What is an example of conditional distribution?

Suppose you’re selling computers, and you record the type of computer and gender for each sale. Now imagine that you want to assess the dispersal of computer types for only female customers. That’s an example of a conditional distribution. We’re conditioning computer types on the gender variable value of female.

How do you solve a conditional distribution?

First, to find the conditional distribution of X given a value of Y, we can think of fixing a row in Table 1 and dividing the values of the joint pmf in that row by the marginal pmf of Y for the corresponding value. For example, to find pX|Y(x|1), we divide each entry in the Y=1 row by pY(1)=1/2.

#### Is age continuous or discrete?

Mondal[1] suggests that age can be viewed as a discrete variable because it is commonly expressed as an integer in units of years with no decimal to indicate days and presumably, hours, minutes, and seconds.

#### Is hours of sleep discrete or continuous?

Examples: Amount of sleep is a variable. 3, 5, 9 hours of sleep are different values for that variable. Variables can be continuous or discrete.

Frequency distribution table:

Score (X) Frequency (f)
etc. etc.

What is expected value example?

Definition and explanation

Expected value is the probability multiplied by the value of each outcome. For example, a 50% chance of winning \$100 is worth \$50 to you (if you don’t mind the risk). We can use this framework to work out if you should play the lottery.

## How do you find the expected value example?

For example, suppose a there is a 20% chance of 1 inch of rain, a 70% chance of 2 inches of rain, and a 10% chance of 3 inches of rain. We would calculate the expected value for the amount of rain to be: Expected value = 0.2*1 + 0.7*2 + 0.1*3 = 1.9 inches.

## What is the formula for expected value?

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E ( X ) = μ = ∑ x P ( x ) .

What is expectation in probability with example?

Expected value is the probability multiplied by the value of each outcome. For example, a 50% chance of winning \$100 is worth \$50 to you (if you don’t mind the risk). We can use this framework to work out if you should play the lottery.

### What do we mean by conditional expectation?

Conditional expectation: the expectation of a random variable X, condi- tional on the value taken by another random variable Y . If the value of Y affects the value of X (i.e. X and Y are dependent), the conditional expectation of X given the value of Y will be different from the overall expectation of X.

What are the properties of conditional expectation?

#### What is conditional probability explain with an example?

Conditional probability: p(A|B) is the probability of event A occurring, given that event B occurs. For example, given that you drew a red card, what’s the probability that it’s a four (p(four|red))=2/26=1/13. So out of the 26 red cards (given a red card), there are two fours so 2/26=1/13.