(a) The probability that a molecule in the atmosphere is at a height between z and z + dz above the surface of the Earth is proportional to e-z/^ dz (capital Greek lambda). Determine the constant of proportionality. Sketch this distribution.

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(a) The probability that a molecule in the atmosphere is at a height between z and z + dz above the surface of the Earth is
proportional to e-z/A dz (capital Greek lambda). Determine the constant of proportionality. Sketch this distribution.
(b) What is the mean molecular height, i.e. the mean height of a molecule?
(c) What is the variance in the molecular height?
(d) What is the standard deviation in the molecular height?
Transcribed Image Text:(a) The probability that a molecule in the atmosphere is at a height between z and z + dz above the surface of the Earth is proportional to e-z/A dz (capital Greek lambda). Determine the constant of proportionality. Sketch this distribution. (b) What is the mean molecular height, i.e. the mean height of a molecule? (c) What is the variance in the molecular height? (d) What is the standard deviation in the molecular height?
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