## What is the expected value of X?

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.

## What is the expected value of X binomial distribution?

The expected value, or mean, of a binomial distribution, is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.

How do you find the expected value of P and N?

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens: (P(x) * n).

### What is NP expected value?

The mean is often called the “expected value” or the “expectation value”. You expect this value because the probability of getting “heads” is 0.5 and if you toss 10 times you should get 5. To formalize this particular example of the mean, if p is the probability and n the number of events, then the mean is a = np.

### How do you find the expected value in probability?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values. By calculating expected values, investors can choose the scenario most likely to give the desired outcome.

What is expected value of probability distribution?

In a probability distribution , the weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value , usually represented by E(x) .

#### What is the expected value of a probability distribution?

How do you find the expected value of the given probability distribution?

To find the expected value or long term average, μ, simply multiply each value of the random variable by its probability and add the products.

## What is the expected value of the Pascal distribution?

This equation computes the mean, or expected value E(X) E ( X) of a Pascal Distribution. The Pascal Distribution is a special case of the negative binomial distribution in which the stopping time parameter, r is an integer. The inputs to this computation of the Expected Value (mean) are:

## What is Pascal distribution with parameters r and P?

The Pascal distribution with parameters r and p arises naturally in the scheme of the Bernoulli trial (cf. Bernoulli trials) with probability of “success” p and of “failure” 1 − p , as the distribution of the number of failures up to the occurrence of the r – th success.

How do you find the variance of a Pascal distribution?

The generating function and characteristic function of a Pascal distribution are f ( t) = p r ( 1 − q e i t) − r, q = 1 − p. The mathematical expectation and the variance are r q / p and r q / p 2 , respectively.

### How do you find the beta distribution of a Pascal distribution?

The distribution function of a Pascal distribution for k = 0, 1 … is given by the formula where on the right-hand side there stands the value of the beta-distribution function at the point p ( here B ( r, k + 1) is the beta-function). Using this relation one can define F ( k) for all r > 0 .