Unizor - Statistical Distribution - Task D - Precipitation
Channel: Zor Shekhtman on UNIZOR Education
Date: 2016-06-14

Unizor - Creative Minds through Art of Mathematics - Math4Teens

In order to determine if the claims about climate change are true or false, the monthly precipitation data at New York's Central Park have been gathered from the official Web site New York Historical Monthly Precipitation for the period from 1906 to 2015.
Based on these data, determine for each decade (10-year period) the mean, standard deviation and 95% certainty interval of the level of precipitation for each month of the year as well as for annualized levels.
Make a judgement about validity of the claims of New York climate change by comparing mean precipitation level in different months between two decades, 1906-1915 and 2006-2015 separated by a century. Consider a comparison of a difference between levels with zero.

Let random variables ξ1906, ξ1907,...ξ1915, represent January precipitation during 1906-1915 years (calculations for other months and annualized precipitation are similar).
It is reasonable to assume that all of them are independent and have identical normal distribution with mathematical expectation μ190# and variance σ²190#, which represent our mathematical model of the precipitation during these ten years.

Random variable
ξ1 = (ξ1906+...+ξ1915)/10
represents average January precipitation during 1906-1915 decade. It's expectation is μ1=μ190# and its variance equals to σ²1=σ²190#/10.

Analogously, independent and identically distributed random variables ξ2006, ξ2007,...ξ2015, represent January precipitation during 2006-2015 years, each having mathematical expectation μ200# and variance σ²200#, which represent our mathematical model of the precipitation during these ten years.

Random variable
ξ2 = (ξ2006+...+ξ2015)/10
represents average January precipitation during 2006-2015 decade. It's expectation is μ2=μ200# and its variance equals to σ²2=σ²200#/10.

On the simplest level, to determine the validity of the claims about climate change during 20th century, we can compare mathematical expectations
μ1 = E(ξ1) and μ2 = E(ξ2)
that is, mean precipitations in the beginning of 20th and 21st centuries.
If they are different (or, which is the same, if μ2−μ1 ≠ 0), we have a confirmation of a shift in the precipitation. Based on this, we can calculate absolute and relative increase or decrease of precipitation during this 100 years period.