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faltersainse [42]
3 years ago
12

What is the significance of the mean of a probability​ distribution?

Mathematics
1 answer:
kari74 [83]3 years ago
4 0

Answer:

See explanation below.

Step-by-step explanation:

If we have a continuous variable the expected value is defined as:

E(X) = \mu = \int_{a}^b x f(x) dx

Where a and b are the limits for the distribution and f(x) represent the density function.

If we have a discrete random variable X, the expected value is defined as:

E(X) = \sum_{i=1}^n x_i P(X_i)

The mean is the most common measure of central tendency in order to describe a probability distribution.

The expected value also represent the first central moment of the random variable defined as:

\mu_1= E[(X-E[X])^1] =\int_{-\infty}^{\infty} (x-\mu)^n f(x) dx

If we assum that X is a continuous random variable.

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Answer:

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Step-by-step explanation:

Any inequality that does not include the "or equal to" case will be graphed with a dashed line.

<h3>Application</h3>

The "or equal to" case is included when the inequality symbol is one of ≤ or ≥. When symbols > or < are used, the boundary line of the solution space is dashed (or the end point on the number line is an open circle).

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2 years ago
What is a true statement about negative exponents?
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Answer:

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Step-by-step explanation:

Let's assume that you wanted to know what x^{-2} is.

To find it, you would take the reciprocal of the x amount. So x^{-2} becomes \frac{1}{x^{2}}.

This works because of the nature of exponents. Exponents represent the number of times you are multiplying a value by itself. So a^{3} would be equal to a · a · a. To increase the exponent, you increase the number of times the value is multiplied by itself: To increase a^{3} to a^{5}, you would have to multiply a with a^{3} two more times (a · a · a · a · a). To decrease the exponent, you must divide the value by itself. So to decrease a^{5} to a^{2}, you would have to divide a^{5} by a 3 times.

If the exponent is 0, the value is equal to 1. But you can still decrease the exponent into negative numbers. You just divide 1 by a the desired amount of times: \frac{1}{a^{3}} means that you are dividing 1 by a 3 times.

Hope this helps.

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