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‘Bell curve’ often refers to a Gaussian distribution. That distribution is so common that it’s also called the normal distribution. It’s very common because it emerges any time you’re looking at the sum of many things from a single distribution: I.e. lots of tiny fluctuations which, under the Central Limit Theorem, add up to a Gaussian distribution.

Although they look bell-shaped, none of the examples here are actually Gaussian, however. They have somewhat more complicated causes.

Of the three, the Maxwell distribution comes closest. It’s a little higher in the upper tail than a Gaussian, and goes to zero at zero unlike a Gaussian. (The distribution of velocities along a single axis is Gaussian) Physically, this is caused by phase space: to have speed exactly zero, a particle needs all of Vx, Vy and Vz zero, which is very unlikely.

The other two distributions are even further from Gaussian.

The Wien distributions do have a quantum-mechanical reason, though it’s somewhat specific to the underlying Planck radiation: it comes from the need for the higher energy (lower wavelength) radiation to come in specific-sized quanta. This causes the increase coming in from the left to have to turn over to reach zero at zero.

The Beta decay shape also doesn’t come from combing lots of small effects. Rather, it also comes from phase space: when the beta particle has a middling energy, there are lots of possibilities for the direction and energy of the nucleus and neutrino. At very high or very low energies, however, there are much fewer possibilities: everything has to line up just right, so the probability is lower.

Many physical distributions, particularly in thermal or stochastic physics, do have a “round central hump, declining on both sides” look due to the limits of the physically possible: some principle, like quantization or conservation of energy, makes it very unlikely or even impossible past some value. In thermal physics, this is often the laws of probability: you’re combining a bunch of little effects, it’s unlikely they’ll all go one way or the other. Having all the events push you out into one tail or the other is unlikely, and the further out you go, the less likely that lineup gets. So it’s common for a physical distribution to slope away from a central peak that’s roughly where all the +/- fluctuations have cancelled out.

‘Bell curve’ often refers to a Gaussian distribution. That distribution is so common that it’s also called the normal distribution. It’s very common because it emerges any time you’re looking at the sum of many things from a single distribution: I.e. lots of tiny fluctuations which, under the Central Limit Theorem, add up to a Gaussian distribution.

Although they look bell-shaped, none of the examples here are actually Gaussian, however. They have somewhat more complicated causes.

Of the three, the Maxwell distribution comes closest. It’s a little higher in the upper tail than a Gaussian, and goes to zero at zero unlike a Gaussian. (The distribution of velocities along a single axis is Gaussian) Physically, this is caused by phase space: to have speed exactly zero, a particle needs all of Vx, Vy and Vz zero, which is very unlikely.

The other two distributions are even further from Gaussian.

The Wien distributions do have a quantum-mechanical reason, though it’s somewhat specific to the underlying Planck radiation: it comes from the need for the higher energy (lower wavelength) radiation to come in specific-sized quanta. This causes the increase coming in from the left to have to turn over to reach zero at zero.

The Beta decay shape also doesn’t come from combining lots of small effects. Rather, it also comes from phase space: when the beta particle has a middling energy, there are lots of possibilities for the direction and energy of the nucleus and neutrino. At very high or very low energies, however, there are much fewer possibilities: everything has to line up just right, so the probability is lower.

Many physical distributions, particularly in thermal or stochastic physics, do have a “round central hump, declining on both sides” look due to the limits of the physically possible: some principle, like quantization or conservation of energy, makes it very unlikely or even impossible past some value. In thermal physics, this is often the laws of probability: you’re combining a bunch of little effects, it’s unlikely they’ll all go one way or the other. Having all the events push you out into one tail or the other is unlikely, and the further out you go, the less likely that lineup gets. So it’s common for a physical distribution to slope away from a central peak that’s roughly where all the +/- fluctuations have cancelled out.

‘Bell curve’ often refers to a Gaussian distribution. That distribution is so common that it’s also called the normal distribution. It’s very common because it emerges any time you’re looking at the sum of many things from a single distribution: I.e. lots of tiny fluctuations which, under the Central Limit Theorem, add up to a Gaussian distribution.

Although they look bell-shaped, none of the examples here are actually Gaussian, however. They have somewhat more complicated causes.

Of the three, the Maxwell distribution comes closest. It’s a little higher in the tails than a Gaussian. Physically, all the collisions aren’t quite equal: faster particles collide a bit more often, which tends to populate the tails a bit more.

The other two distributions are even further from Gaussian.

The Wien distributions do have a quantum-mechanical reason, though it’s somewhat specific to the underlying Planck radiation: it comes from the need for the higher energy (lower wavelength) radiation to come in specific-sized quanta. This causes the increase coming in from the left to have to turn over to reach zero at zero.

The Beta decay shape also doesn’t come from combing lots of small effects. Rather, it comes from phase space: when the beta particle has a middling energy, there are lots of possibilities for the direction and energy of the nucleus and neutrino. At very high or very low energies, however, there are much fewer possibilities: everything has to line up just right, so the probability is lower.

Still, many physical distributions, particularly in thermal or stochastic physics, do have a “round central hump, declining on both sides” look. When you’re combining a bunch of little effects, it’s unlikely they’ll all go one way or the other: having all the events push you out into one tail or the other is unlikely, and the further out you go, the less likely that lineup gets. So it’s common for a physical distribution to slope away from a central peak that’s roughly where all the +/- fluctuations have cancelled out.

‘Bell curve’ often refers to a Gaussian distribution. That distribution is so common that it’s also called the normal distribution. It’s very common because it emerges any time you’re looking at the sum of many things from a single distribution: I.e. lots of tiny fluctuations which, under the Central Limit Theorem, add up to a Gaussian distribution.

Although they look bell-shaped, none of the examples here are actually Gaussian, however. They have somewhat more complicated causes.

Of the three, the Maxwell distribution comes closest. It’s a little higher in the upper tail than a Gaussian, and goes to zero at zero unlike a Gaussian. (The distribution of velocities along a single axis is Gaussian) Physically, this is caused by phase space: to have speed exactly zero, a particle needs all of Vx, Vy and Vz zero, which is very unlikely.

The other two distributions are even further from Gaussian.

The Wien distributions do have a quantum-mechanical reason, though it’s somewhat specific to the underlying Planck radiation: it comes from the need for the higher energy (lower wavelength) radiation to come in specific-sized quanta. This causes the increase coming in from the left to have to turn over to reach zero at zero.

The Beta decay shape also doesn’t come from combing lots of small effects. Rather, it also comes from phase space: when the beta particle has a middling energy, there are lots of possibilities for the direction and energy of the nucleus and neutrino. At very high or very low energies, however, there are much fewer possibilities: everything has to line up just right, so the probability is lower.

Many physical distributions, particularly in thermal or stochastic physics, do have a “round central hump, declining on both sides” look due to the limits of the physically possible: some principle, like quantization or conservation of energy, makes it very unlikely or even impossible past some value. In thermal physics, this is often the laws of probability: you’re combining a bunch of little effects, it’s unlikely they’ll all go one way or the other. Having all the events push you out into one tail or the other is unlikely, and the further out you go, the less likely that lineup gets. So it’s common for a physical distribution to slope away from a central peak that’s roughly where all the +/- fluctuations have cancelled out.

‘Bell curve’ often refers to a Gaussian distribution. That distribution is so common that it’s also called the normal distribution. It’s very common because it emerges any time you’re looking at the sum of many things from a single distribution: I.e. lots of tiny fluctuations which, under the Central Limit Theorem, add up to a Gaussian distribution.

Although they look bell-shaped, none of the examples here are actually Gaussian, however. They have somewhat more complicated causes.

Of the three, the Maxwell distribution comes closest. It’s a little higher in the tails than a Gaussian. Physically, all the collisions aren’t quite equal: faster particles collide a bit more often, which tends to populate the tails a bit more.

The other two distributions are even further from Gaussian.

The Beta decay shape doesn’t come from combined lots of small effects. Rather, it comes from phase space: when the beta particle has a middling energy, there are lots of possibilities for the direction and energy of the nucleus and neutrino. At very high or very low energies, however, there are much fewer possibilities: everything has to line up just right, so the probability is lower.

Still, many physical distributions do have a “round central hump, declining on both sides” look. When you’re combining a bunch of little effects, it’s unlikely they’ll all go one way or the other: having all the events push you out into one tail or the other is unlikely, and the further out you go, the less likely that lineup gets. So it’s common for a physical distribution to slope away from a central peak that’s roughly where all the +/- fluctuations have cancelled out.

‘Bell curve’ often refers to a Gaussian distribution. That distribution is so common that it’s also called the normal distribution. It’s very common because it emerges any time you’re looking at the sum of many things from a single distribution: I.e. lots of tiny fluctuations which, under the Central Limit Theorem, add up to a Gaussian distribution.

Although they look bell-shaped, none of the examples here are actually Gaussian, however. They have somewhat more complicated causes.

Of the three, the Maxwell distribution comes closest. It’s a little higher in the tails than a Gaussian. Physically, all the collisions aren’t quite equal: faster particles collide a bit more often, which tends to populate the tails a bit more.

The other two distributions are even further from Gaussian.

The Wien distributions do have a quantum-mechanical reason, though it’s somewhat specific to the underlying Planck radiation: it comes from the need for the higher energy (lower wavelength) radiation to come in specific-sized quanta. This causes the increase coming in from the left to have to turn over to reach zero at zero.

The Beta decay shape also doesn’t come from combing lots of small effects. Rather, it comes from phase space: when the beta particle has a middling energy, there are lots of possibilities for the direction and energy of the nucleus and neutrino. At very high or very low energies, however, there are much fewer possibilities: everything has to line up just right, so the probability is lower.

Still, many physical distributions, particularly in thermal or stochastic physics, do have a “round central hump, declining on both sides” look. When you’re combining a bunch of little effects, it’s unlikely they’ll all go one way or the other: having all the events push you out into one tail or the other is unlikely, and the further out you go, the less likely that lineup gets. So it’s common for a physical distribution to slope away from a central peak that’s roughly where all the +/- fluctuations have cancelled out.