Pure Programmer
Project: Central Limit Theorem
The [[Central_limit_theorem#Classical_CLT|Central Limit Theorem]] states that if we take random samples of size N from any distribution of independent random variables, that the distribution of sample averages (`bar X`) should fall in a normal distribution regardless of the type of distribution of the samples. For example our typical random number generators use a uniform, not normal, distribution. But if we take samples of size N, average them, then we should get a sample distribution that is normal with a mean that is the same as our sample source distribution mean and a standard deviation that is equal to the standard deviation of our sample source distribution divided by `sqrt(N)`.
Write a program that accepts a sample size N on the command line and the number of samples to collect M. Then generate the mean (`bar X`) of a sample of size N from random float values [0, 20). Do this M times maintaining a running count of the occurances in an array of 20 by using `lfloor bar X rfloor` (use floor() or int() function) to select the array element to increment. Output a tab-delimited table with the array index in column 1 and the count in column 2. This output can easily be piped into the Histogram project to get a simple graph that should look like a normal distribution centered on 10.0. Notice how as the sample size increases, the standard deviation shrinks?
Output
$ rustc CentralLimitTheorem.rs
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:31
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:38
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:13:5
|
13 | if args.len() != 3 {
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `exit` in this scope
--> CentralLimitTheorem.rs:15:3
|
15 | exit(1);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::process::exit;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:17:29
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:17:51
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:18:34
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:18:56
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `random` in this scope
--> CentralLimitTheorem.rs:36:13
|
36 | sum += random(0,sampleMax) * (sampleMax) as f64;
| ^^^^^^ not found in this scope
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:41:15
|
41 | meanCounts[(mean) as isize] += 1;
| ^^^^^^^^^^^^^^^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:48:57
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error: aborting due to 11 previous errors
Some errors have detailed explanations: E0277, E0425.
For more information about an error, try `rustc --explain E0277`.
$ rustc CentralLimitTheorem.rs
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:31
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:38
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:13:5
|
13 | if args.len() != 3 {
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `exit` in this scope
--> CentralLimitTheorem.rs:15:3
|
15 | exit(1);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::process::exit;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:17:29
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:17:51
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:18:34
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:18:56
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `random` in this scope
--> CentralLimitTheorem.rs:36:13
|
36 | sum += random(0,sampleMax) * (sampleMax) as f64;
| ^^^^^^ not found in this scope
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:41:15
|
41 | meanCounts[(mean) as isize] += 1;
| ^^^^^^^^^^^^^^^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:48:57
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error: aborting due to 11 previous errors
Some errors have detailed explanations: E0277, E0425.
For more information about an error, try `rustc --explain E0277`.
$ rustc CentralLimitTheorem.rs
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:31
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:38
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:13:5
|
13 | if args.len() != 3 {
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `exit` in this scope
--> CentralLimitTheorem.rs:15:3
|
15 | exit(1);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::process::exit;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:17:29
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:17:51
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:18:34
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:18:56
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `random` in this scope
--> CentralLimitTheorem.rs:36:13
|
36 | sum += random(0,sampleMax) * (sampleMax) as f64;
| ^^^^^^ not found in this scope
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:41:15
|
41 | meanCounts[(mean) as isize] += 1;
| ^^^^^^^^^^^^^^^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:48:57
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error: aborting due to 11 previous errors
Some errors have detailed explanations: E0277, E0425.
For more information about an error, try `rustc --explain E0277`.
$ rustc CentralLimitTheorem.rs
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:31
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error: unknown format trait `d`
--> CentralLimitTheorem.rs:48:38
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^
|
= note: the only appropriate formatting traits are:
- ``, which uses the `Display` trait
- `?`, which uses the `Debug` trait
- `e`, which uses the `LowerExp` trait
- `E`, which uses the `UpperExp` trait
- `o`, which uses the `Octal` trait
- `p`, which uses the `Pointer` trait
- `b`, which uses the `Binary` trait
- `x`, which uses the `LowerHex` trait
- `X`, which uses the `UpperHex` trait
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:13:5
|
13 | if args.len() != 3 {
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `exit` in this scope
--> CentralLimitTheorem.rs:15:3
|
15 | exit(1);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::process::exit;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:17:29
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:17:51
|
17 | let mut sampleSize:isize = Utils.stoiWithDefault(args[1], 10);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find value `Utils` in this scope
--> CentralLimitTheorem.rs:18:34
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^^ not found in this scope
error[E0425]: cannot find value `args` in this scope
--> CentralLimitTheorem.rs:18:56
|
18 | let mut numberOfSamples:isize = Utils.stoiWithDefault(args[2], 100);
| ^^^^ not found in this scope
|
help: consider importing this function
|
8 + use std::env::args;
|
error[E0425]: cannot find function `random` in this scope
--> CentralLimitTheorem.rs:36:13
|
36 | sum += random(0,sampleMax) * (sampleMax) as f64;
| ^^^^^^ not found in this scope
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:41:15
|
41 | meanCounts[(mean) as isize] += 1;
| ^^^^^^^^^^^^^^^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error[E0277]: the type `[isize]` cannot be indexed by `isize`
--> CentralLimitTheorem.rs:48:57
|
48 | println!("{}", format!("{0:d}\t{1:d}", i, meanCounts[i]));
| ^ slice indices are of type `usize` or ranges of `usize`
|
= help: the trait `SliceIndex<[isize]>` is not implemented for `isize`
= help: the trait `SliceIndex<[T]>` is implemented for `usize`
= note: required for `Vec<isize>` to implement `Index<isize>`
error: aborting due to 11 previous errors
Some errors have detailed explanations: E0277, E0425.
For more information about an error, try `rustc --explain E0277`.