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html 1155510 John Blischak 2019-07-15 Build site.
Rmd 4f254dd John Blischak 2019-07-15 Add some statistics examples from Mastering ’Metrics

Exploring some properties of variance.

The variance of a difference between two statistically independent variables is the sum of their variances. (Mastering ’Metrics, p. 44)

Using two normal random variables:

a <- rnorm(100, sd = 2)
var(a)
[1] 3.699953
b <- rnorm(100, sd = 3)
var(b)
[1] 11.28001
var(a - b)
[1] 15.37946
var(a) + var(b)
[1] 14.97996

Using two Poisson random variables:

a <- rpois(100, lambda = 2)
var(a)
[1] 2.343434
b <- rpois(100, lambda = 3)
var(b)
[1] 2.672323
var(a - b)
[1] 4.955152
var(a) + var(b)
[1] 5.015758

Using a normal and a Poisson random variable:

a <- rnorm(100, sd = 2)
var(a)
[1] 3.729297
b <- rpois(100, lambda = 3)
var(b)
[1] 2.474646
var(a - b)
[1] 5.922479
var(a) + var(b)
[1] 6.203944

sessionInfo()
R version 4.3.3 (2024-02-29 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 11 x64 (build 22631)

Matrix products: default


locale:
[1] LC_COLLATE=English_United States.utf8 
[2] LC_CTYPE=English_United States.utf8   
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.utf8    

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] workflowr_1.7.1

loaded via a namespace (and not attached):
 [1] vctrs_0.6.5       httr_1.4.7        cli_3.6.2         knitr_1.45       
 [5] rlang_1.1.3       xfun_0.42         stringi_1.8.3     processx_3.8.3   
 [9] promises_1.2.1    jsonlite_1.8.8    glue_1.7.0        rprojroot_2.0.4  
[13] git2r_0.33.0      htmltools_0.5.7   httpuv_1.6.14     ps_1.7.6         
[17] sass_0.4.8        fansi_1.0.6       rmarkdown_2.26    jquerylib_0.1.4  
[21] tibble_3.2.1      evaluate_0.23     fastmap_1.1.1     yaml_2.3.8       
[25] lifecycle_1.0.4   whisker_0.4.1     stringr_1.5.1     compiler_4.3.3   
[29] fs_1.6.3          pkgconfig_2.0.3   Rcpp_1.0.12       rstudioapi_0.15.0
[33] later_1.3.2       digest_0.6.34     R6_2.5.1          utf8_1.2.4       
[37] pillar_1.9.0      callr_3.7.5       magrittr_2.0.3    bslib_0.6.1      
[41] tools_4.3.3       cachem_1.0.8      getPass_0.2-4