Q: A distribution is symmetrical if the tails on both ends of the density curve that represents it are close to identical?

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I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.

The probability density functions are different in shape and the domain. The domain of the beta distribution is from 0 to 1, while the normal goes from negative infinite to positive infinity. The shape of the normal is always a symmetrical, bell shape with inflection points on either sides of the mean. The beta distribution can be a variety of shapes, symmetrical half circle, inverted (cup up) half circle, or asymmetrical shapes. Normal distribution has many applications in classical hypothesis testing. Beta has many applications in Bayesian analysis. The uniform distribution is considered a specialized case of the beta distribution. See related links.

Uneven distribution

what is density curve

Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.

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Yes, CF4 (carbon tetrafluoride) has a symmetrical distribution because the molecule is tetrahedral with four identical fluorine atoms bonded to a central carbon atom. This symmetry results in an equal distribution of electron density around the central atom.

non polar.

Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).

The bond between two Br atoms is considered nonpolar because both atoms are the same element with identical electronegativity values. This means that the electrons are equally shared between the two atoms, resulting in a symmetrical distribution of electron density across the bond.

Ethane is a nonpolar molecule because it has a symmetrical linear shape, with carbon atoms bonded to hydrogen atoms. This symmetrical distribution of electron density results in a net dipole moment of zero, making the molecule nonpolar.

I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.

No, a bromine-bromine bond is nonpolar because bromine atoms have similar electronegativities. This results in a symmetrical distribution of electron density around the atoms.

10,486.22 this is the density population and this is the distribution population 2,00465.789

The dipole moment of ozone is about 0.53 Debye. Ozone has a bent molecular structure with an uneven distribution of electron density, creating a permanent dipole moment.

probability density distribution

The probability density functions are different in shape and the domain. The domain of the beta distribution is from 0 to 1, while the normal goes from negative infinite to positive infinity. The shape of the normal is always a symmetrical, bell shape with inflection points on either sides of the mean. The beta distribution can be a variety of shapes, symmetrical half circle, inverted (cup up) half circle, or asymmetrical shapes. Normal distribution has many applications in classical hypothesis testing. Beta has many applications in Bayesian analysis. The uniform distribution is considered a specialized case of the beta distribution. See related links.