1. Drawing balls without replacement (20 pts). Suppose that we have an urn containing one red ball and n − 1 white balls. Each time we draw a ball at random from the urn without replacement (so after the n-th drawing, there is no ball left in the urn). X i = 1 if the i-th ball is red, 0 otherwise.

2. Polya’s urn. Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random from the urn. If it is red, we put the drawn ball plus another red ball into the urn. If it is blue, we put the drawn ball plus another blue ball into the urn. We then repeat this process. At the n-th stage, we draw a ball at random from the urn with n+1 balls, note its color, and put the ...

Two trials using a total of 1,484 Ross male broilers were conducted to study the effect of air velocities of 180 and 120 m/min versus still air (<15 m/min) on BW gain (BWG) and feed:gain from 3 to 7 wk of age. Broilers were raised in a common environment to 3 wk of age. The experimental facility was a closed sided house containing eight wind tunnel floor pens and six floor pens. There were two ...

Dabigatran etexilate, a double prodrug of dabigatran, is a reversible, competitive, direct thrombin inhibitor that has been approved for use in many countries. A recent guideline from the European Medicines Agency on drug-drug interactions proposed dabigatran etexilate as a sensitive in vivo and in vitro probe substrate for intestinal P-glycoprotein (P-gp) inhibition. We therefore performed a s...

Solutions to Exercise Set #4 1. Optical communication channel. Let the signal input to an optical channel be given by X = 1 with probability 1 2 10 with probability 1 2. Find y * and the corresponding probability of error.