diff --git a/ex-1/bootstrap.c b/ex-1/bootstrap.c
index ca69985..f8388d3 100644
--- a/ex-1/bootstrap.c
+++ b/ex-1/bootstrap.c
@@ -43,8 +43,8 @@ size_t mean_index(gsl_vector *v, double x) {
 /* Computes the half-sample mode (also called the Robertson-Cryer
  * mode estimator) of the sample `x` containing `n` observations. 
  *
- * It is based on repeatedly finding the modal interval (interval
- * containing the most observations) of half of the sample.
+ * It is based on repeatedly finding the half modal interval (smallest
+ * interval containing half of the observations) of the sample.
  * This implementation is based on the `hsm()` function from the
  * modeest[1] R package.
  *
@@ -129,7 +129,7 @@ double gauss_kde(double x, void * params) {
    * by the sample variance times a factor which
    * depends on the number of points and dimension.
    */
-  double bw = p.var * pow((double)p.n*3.0/4, -2.0/5);
+  double bw = 0.4 * p.var * pow((double)p.n*3.0/4, -2.0/5);
 
   double sum = 0;
   for (size_t i = 0; i < p.n; i++)
diff --git a/ex-1/main.c b/ex-1/main.c
index af414f1..293e052 100644
--- a/ex-1/main.c
+++ b/ex-1/main.c
@@ -20,7 +20,7 @@ int main(int argc, char** argv) {
   gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
 
   // prepare histogram
-  size_t samples = 100000;
+  size_t samples = 50000;
   double* sample = calloc(samples, sizeof(double));
   double min = -10;
   double max =  10;
@@ -40,7 +40,7 @@ int main(int argc, char** argv) {
   }
   fprintf(stderr, "done\n");
 
-  // sort the sample: needed for HSM and KS tests
+  // sort the sample: needed for HSM and ks tests
   qsort(sample, samples, sizeof(double), &cmp_double);
 
 
@@ -88,7 +88,7 @@ int main(int argc, char** argv) {
 
   // print the results
   fprintf(stderr, "\n## Results\n");
-  fprintf(stderr, "expected mode: %.7f\n", mode_e);
+  fprintf(stderr, "expected mode: %.8f\n", mode_e);
   fprintf(stderr, "observed mode: %.4f±%.4f\n", mode_o.n, mode_o.s);
 
   // t-test
diff --git a/ex-1/tests.c b/ex-1/tests.c
index f080079..91b86d1 100644
--- a/ex-1/tests.c
+++ b/ex-1/tests.c
@@ -108,7 +108,7 @@ double numeric_mode(double min, double max,
       x      = gsl_min_fminimizer_x_minimum(s);
       min    = gsl_min_fminimizer_x_lower(s);
       max    = gsl_min_fminimizer_x_upper(s);
-      status = gsl_min_test_interval(min, max, prec, prec);
+      status = gsl_min_test_interval(min, max, 0, prec);
 
   } while (status == GSL_CONTINUE && iter < max_iter);