Practice Set 6.1

library(tidyverse)

Warning: package 'tidyverse' was built under R version 4.3.3

Warning: package 'tibble' was built under R version 4.3.3

Warning: package 'tidyr' was built under R version 4.3.3

Warning: package 'readr' was built under R version 4.3.3

Warning: package 'purrr' was built under R version 4.3.3

Warning: package 'dplyr' was built under R version 4.3.3

Warning: package 'stringr' was built under R version 4.3.3

Warning: package 'forcats' was built under R version 4.3.3

Warning: package 'lubridate' was built under R version 4.3.3

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   4.0.1     ✔ tibble    3.2.1
✔ lubridate 1.9.4     ✔ tidyr     1.3.1
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(purrrfect)

Attaching package: 'purrrfect'

The following objects are masked from 'package:base':

    replicate, tabulate

Question 9

(sim1 <- parameters(~lambda,c(.5,1,1.5,2))
  
  %>%add_trials(10000)
  %>%mutate(x = rexp(40000,lambda),y = rexp(40000,lambda),u_sim = pmap_dbl(list(x,y),\(x,y) x+y),u = dgamma(u_sim,2,lambda))
)

# A tibble: 40,000 × 6
   lambda .trial      x     y u_sim      u
    <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>
 1    0.5      1 0.670  1.15   1.82 0.183 
 2    0.5      2 5.13   3.86   8.98 0.0252
 3    0.5      3 0.0128 1.42   1.43 0.175 
 4    0.5      4 2.06   1.63   3.69 0.146 
 5    0.5      5 0.512  8.73   9.24 0.0227
 6    0.5      6 1.15   1.23   2.38 0.181 
 7    0.5      7 1.59   0.438  2.03 0.184 
 8    0.5      8 2.33   5.13   7.46 0.0447
 9    0.5      9 0.725  3.00   3.73 0.145 
10    0.5     10 4.11   0.451  4.56 0.117 
# ℹ 39,990 more rows

(ggplot(aes(x=u_sim),data=sim1)
+ geom_histogram(aes(y =after_stat(density)),
fill = 'red',
binwidth = 0.05, center = 0.05)
+ geom_line(aes(y = u), col = 'blue', linewidth=1)
+ labs(y='Beta Density', x= 'y')
+ theme_classic(base_size = 12)
+ facet_grid(~lambda,labeller = label_both,scales = "free")
)