Binomial distribution
In general, if the random variable $X$ follows the binomial distribution with parameters $n \in \mathbb{N}$ and $p \in [0,1]$, we write $X \simeq B(n, p)$. The probability of getting exactly $k$ successes in n independent Bernoulli trials is given by the probability mass function:
$$
Pr(X=k) = \binom{n}{k}p^k(1−p)^{n−k}
$$
for $k=0,1, \ldots n$ and $0$ else.
From a technical point of view, this example uses two boards which are connected by `board1.addChild(board)`.
Web references:
// Define the ids of your boards in BOARDID0, BOARDID1,...
const board1 = JXG.JSXGraph.initBoard(BOARDID0, {
boundingbox: [-0.3, 0, 1.3, -4],
axis: false
});
var prob = board1.create('slider', [
[0, -2],
[1, -2],
[0, .5, 1]
], {
name: 'p'
});
const board = JXG.JSXGraph.initBoard(BOARDID1, {
boundingbox: [-1, 1.1, 21, -.1],
axis: true,
showCopyright: false
});
board1.addChild(board);
for (let i = 0; i <= 20; i++) {
board.create('point', [i, () => binomial(20, i, prob.Value())], {
name: ''
});
}
var f = board.create('functiongraph', [function(x) {
var n, dist = 0;
for (n = 0; n < 20 + 1; n++) {
if (x < n) {
return dist;
}
dist = dist + binomial(20, n, prob.Value());
}
return dist;
}]);
function binomial(n, k, p) {
var x, p1 = 1,
p2 = 1,
coeff = 1;
for (x = n - k + 1; x < n + 1; x++) {
coeff *= x;
}
for (x = 1; x < k + 1; x++) {
coeff /= x;
}
for (x = 0; x < k; x++) {
p1 *= p;
}
for (x = 0; x < n - k; x++) {
p2 *= (1 - p);
}
return coeff * p1 * p2;
}
This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.