# Pre-Class

Matlab code for the pre-class activity:

## Code

```n_data=100;
x_init=betarnd(2.5,5,1,n_data);
nresamp=100000;
out_val=zeros(1,nresamp);
for aa=1:nresamp
xx=x_init(randsample(n_data,n_data,true));
[y,x] =hist(xx,100);
out_val(aa) =  x(find(cumsum(y)/sum(y) >=.75,1)) - x(find(cumsum(y)/sum(y) >=0.25,1));
end
hist(out_val,50);
mu=mean(out_val)
sigma=std(out_val)

n_data=100;
x_init=betarnd(2.5,5,1,n_data);
nresamp=100000;
out_val=zeros(1,nresamp);
for aa=1:nresamp
xx=betarnd(3,2,1,n_data);
[y,x] =hist(xx,100);
out_val(aa) =x(find(cumsum(y)/sum(y) >=.75,1)) - x(find(cumsum(y)/sum(y) >=0.25,1));
end
figure
hist(out_val,50);
mu=mean(out_val)
sigma=std(out_val)

act_val = betainv(0.75,2.5,5) - betainv(0.25,2.5,5)
```

## Output

For the bootstrap estimation:

```mu =

0.210450100797775

sigma =

0.028586856472617
```

and for the resampled estimate:

```mu =

0.299897695902584

sigma =

0.033799773359941
```

The actual value is:

```
act_val =

0.232952354263591
```

# In Class

Done with Dan

## Matlab Code

```n_data=100;
x_init=betarnd(3,2,1,n_data);
nresamp=100000;
out_val=zeros(1,nresamp);
xrng=linspace(0,1,1000);
for aa=1:nresamp
xx=x_init(randsample(n_data,n_data,true));
out_val(aa) =  sum(exp(-1.*xrng).*(hist(xx,xrng)/sum(hist(xx,xrng))));
end
S=sum(exp(-1.*xrng).*hist(x_init,xrng)/sum(hist(x_init,xrng)))
hist(out_val,50);
mu=mean(out_val)
sigma=std(out_val)

n_data=100;
x_init=betarnd(3,2,1,n_data);
S=sum(exp(-1.*xrng).*hist(x_init,xrng)/sum(hist(x_init,xrng)))
nresamp=100000;
out_val=zeros(1,nresamp);
for aa=1:nresamp
xx=betarnd(3,2,1,n_data);
out_val(aa) = sum(exp(-1*xrng).*(hist(xx,xrng)/sum(hist(xx,xrng))));
end
figure
hist(out_val,50);
mu=mean(out_val)
sigma=std(out_val)
```

## Results

For the bootstrap estimation:

```mu =

0.558731122219118

sigma =

0.0110396392531490
```

and for the resampled estimate:

```mu =

0.560064580617217

sigma =

0.011525181525111
```