Question

8.9 Let Xt be a standard Brownian motion. Compute the following conditional probability: P{X2 > 0 | X1 > 0}. Are the events {X1 > 0} and {X2 > 0} independent?

          8.9 Let Xt be a standard Brownian motion. Compute the following conditional probability:

P{X2 > 0 | X1 > 0}.

Are the events {X1 > 0} and {X2 > 0} independent?

Added by Miriam C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

03/31/2023

Step 1

We can write the joint distribution as: $$ f_{X_1, X_2}(x_1, x_2) = \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\left(-\frac{1}{2(1-\rho^2)}\left(x_1^2 - 2\rho x_1x_2 + x_2^2\right)\right) $$ Now, we want to compute the conditional probability $P(X_2 > 0 | X_1 > 0)$. Using Show more…

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8.9 Let Xt be a standard Brownian motion. Compute the following conditional probability: P{X2 > 0 | X1 > 0}. Are the events {X1 > 0} and {X2 > 0} independent?