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I have come up with the following understanding about Expectation of RV.

Please, correct me if I am wrong.

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$

Continuous Case

If $$X$$ is a continuous random variable with density function $$f_X(x),$$ then the expectation of $$X$$ is $$\displaystyle E(X)=\int_{-\infty}^\infty x\,f_X(x)\,dx$$

If $$Y=g(X)$$ is a function of $$X$$(i.e. a density function)$$,$$ then $$\displaystyle E(Y)=\int_{-\infty}^\infty g(x)\,f_X(x)\,dx$$

Edit:

Definition:

Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the average value of the outcomes.

Expected value of a Random Variable is a value. It is not a probability.

Example:

In case of a dice, if the dice is rolled $$n$$ number of times, the average value of the outcomes would be 3.5.

I have come up with the following understanding about Expectation of RV.

Please, correct me if I am wrong.

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$

Continuous Case

If $$X$$ is a continuous random variable with density function $$f_X(x),$$ then the expectation of $$X$$ is $$\displaystyle E(X)=\int_{-\infty}^\infty x\,f_X(x)\,dx$$

If $$Y=g(X)$$ is a function of $$X$$(i.e. a density function)$$,$$ then $$\displaystyle E(Y)=\int_{-\infty}^\infty g(x)\,f_X(x)\,dx$$

I have come up with the following understanding about Expectation of RV.

Please, correct me if I am wrong.

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$

Continuous Case

If $$X$$ is a continuous random variable with density function $$f_X(x),$$ then the expectation of $$X$$ is $$\displaystyle E(X)=\int_{-\infty}^\infty x\,f_X(x)\,dx$$

If $$Y=g(X)$$ is a function of $$X$$(i.e. a density function)$$,$$ then $$\displaystyle E(Y)=\int_{-\infty}^\infty g(x)\,f_X(x)\,dx$$

Edit:

Definition:

Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the average value of the outcomes.

Expected value of a Random Variable is a value. It is not a probability.

Example:

In case of a dice, if the dice is rolled $$n$$ number of times, the average value of the outcomes would be 3.5.

2 added 113 characters in body

I have come up with the following understanding about Expectation of RV.

Please, correct me if I am wrong.

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$

Continuous Case

If $$X$$ is a continuous random variable with density function $$f_X(x),$$ then the expectation of $$X$$ is $$\displaystyle E(X)=\int_{-\infty}^\infty x\,f_X(x)\,dx$$

If $$Y=g(X)$$ is a function of $$X$$(i.e. a density function)$$,$$ then $$\displaystyle E(Y)=\int_{-\infty}^\infty g(x)\,f_X(x)\,dx$$

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$

I have come up with the following understanding about Expectation of RV.

Please, correct me if I am wrong.

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$

Continuous Case

If $$X$$ is a continuous random variable with density function $$f_X(x),$$ then the expectation of $$X$$ is $$\displaystyle E(X)=\int_{-\infty}^\infty x\,f_X(x)\,dx$$

If $$Y=g(X)$$ is a function of $$X$$(i.e. a density function)$$,$$ then $$\displaystyle E(Y)=\int_{-\infty}^\infty g(x)\,f_X(x)\,dx$$

1

Is my understanding of Expected Value of a Random Variable correct?

Definition: Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times. Expected value of a Random Variable is a value. It is not a probability.

Example: In case of a dice, if the dice is rolled $$n$$ number of times, the value we would see most of the times is 3.5.

Calculation: We don't have to repeat the same experiment $$n$$ number of times to find the expected value of a random variable. It can be done using the random variable and its associated probability distribution. In case of a dice,

$$\sum_{x=1}^6 x(1/6) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5$$