3. Sea X1, …, Xn una m.a. con distribución Bernoulli(θ) con θ∈ (0, 1). Suponga que la informació

Step 1: Modelo y datos. Sea X1,...,Xn i.i.d. Bernoulli(θ) con θ∈(0,1). Prior Uniforme(0,1) = Bet

3. Sea X1, …, Xn una m.a. con distribución Bernoulli(θ) con...

3. Sea $X_1, \dots, X_n$ una m.a. con distribución Bernoulli($\theta$) con $\theta \in (0, 1)$. Suponga que la información inicial se representa mediante una distribución de probabilidad Uniforme(0, 1). Se observa la muestra (1, 0, 0). Como hipótesis tenemos a) Da la hipótesis óptima. $H_1: \theta < 1/4$ $H_2: 1/4 \le \theta \le 3/4$ $H_3: \theta > 3/4$ b) Considerando la función de utilidad $u(a_i, H_j) = I_{\{i=j\}}$ da la acción óptima.

Transcript

00:01 Hello everyone, in this question we have to find the equation of the plane passing through the three points.

00:05 So the formula for the equation of the plane is x minus x1 y minus y1 z minus z1 x2 minus x1 y2 minus y1 z2 minus z1 x3 minus x2 y3 minus y2 z3 minus z2 equal to 0.

00:26 So this point is x1 y1 z1 x2 y2 z2 x3 y3 z3.

00:33 So we will be adding x minus 1 y minus 2 z minus 3 1 1 minus 2 minus 2 minus 5 minus 2 equal to 0.

00:46 So evaluating this determinant we will be adding x minus 1 minus 2 minus 10 minus y minus 2 minus 2 minus 4 plus z minus 3 minus 5 plus 2 equal to 0.

01:02 So x minus 1 minus 12 minus y minus 2 minus 6 plus z minus 3 minus 3 equal to 0.

01:14 So this gives you x minus 1 minus 12 minus minus 6 y plus 12 plus minus 3 z plus 9 equal to 0.

01:25 So we will be having minus 12 x plus 12 plus 6 y minus 12 minus 3 z plus 9 equal to 0.

01:35 So plus 12 and minus 12 will get cancelled.

01:39 So we will be having minus 12 x plus 6 y minus 3 z plus 9 equal to 0.

01:47 So this can be rewritten as 12 x minus 6 y plus 3 z minus 9 equal to 0 is the required equation of plane.

01:58 So the next part is to find the parametric equation and symmetric equation of the plane passing through the point given 3 comma 0 comma 2 and q equal to 1 comma minus 4 comma 0.

02:12 So let us write this the initial point is 1 comma minus 4 comma 0 and the final point is 3 comma 0 comma 2.

02:20 So subtracting final from the initial we will be adding that is 3 comma 0 comma 2 minus 1 comma minus 4 comma 0 we will be adding 2 0 plus 4 will be 4 2 minus 0 is 2...

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