# Code for Monte Carlo simulation: generate samples of given size in R

I started by generating a sample of 500 uniformly-distributed random numbers between 0 and 1 using the code below:

```set.seed(1234)
X<-runif(500, min=0, max=1)
```

Now, I need to write a psuedocode that generates 10000 samples of N=500 for a MC simulation, compute the mean of my newly created X, and store the iteration number and mean value in a result object. I have never attempted this, and so far I have this:

```n.iter <-(10000*500)
results <- matrix (0, n.iter, 4)
```

Finally, once this is accomplished, I'm to run it, then obtain median, mean, and min/max of the accrued sample means and save them to a data frame called MC.table. (Also note, above, I have no idea why there's a "4" in the matrix code --- I'm working off of previous examples). Any advice or help would be greatly appreciated.

EDIT: I have an example that may work, but I don't really understand what's going on with it, so please elaborate on its validity for this:

```Ni <- 10000
n <- 500
c <- 0

for (i in n){
for (j in 1:Ni){
c <- c+ 1
d <- data.frame (x= , y= )
results [c,1] <- c
results [c,2] <- j
results [c,3] <- i
results [c,4] <- something( d\$x, d\$y)
rm (d) } }
```

If you could even take the time to explain what that means, that'd go a long way to helping me! Thanks!

You could try using data.table, a package that can be installed using install.packages("data.table"). With that installed, you would run something like...

```> require(data.table)
> dt <- data.table(x=runif(500*10000),iter=rep(1:500,each=10000))
# x iter
# 1: 0.48293196    1
# 2: 0.61935416    1
# 3: 0.99831614    1
# 4: 0.26944687    1
# 5: 0.38027524    1
# ---
# 4999996: 0.11314160  500
# 4999997: 0.07958396  500
# 4999998: 0.97690312  500
# 4999999: 0.81670765  500
# 5000000: 0.62934609  500
> summaries <- dt[,list(mean=mean(x),median=median(x)),by=iter]
# iter      mean    median
# 1:    1 0.5005310 0.5026592
# 2:    2 0.4971551 0.4950034
# 3:    3 0.4977677 0.4985360
# 4:    4 0.5034727 0.5052344
# 5:    5 0.4999848 0.4971214
# ---
# 496:  496 0.5013314 0.5048186
# 497:  497 0.4955447 0.4941715
# 498:  498 0.4983971 0.4910115
# 499:  499 0.5000382 0.4997024
# 500:  500 0.5009614 0.4988237
> min_o_means <- min(summaries\$mean)
#  0.4914826
```

I think the syntax is fairly straightforward. You may want to look up some of the functions using ? (e.g., ?rep). The lines starting with # are just displaying the generated objects. In data.tables, the number to the left of the : is just the row number and --- indicates rows that are skipped in the display.

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