Question

In: Statistics and Probability

We have three cards. One is red on both sides; one is blue on both sides;...

We have three cards. One is red on both sides; one is blue on both sides; one is red on one side and blue on the other side. The cards are shuffled and their orientation randomized. One card is drawn and placed on the table; the side facing up is blue.

(a) Compute the information content of this observation (that the side facing up is blue.)

(b) Find the prior and posterior probability distributions of the color of the bottom side of the card. (Use Bayes’ theorem to calculate the posterior probability distributions.)

Solutions

Expert Solution

Answer:-

Given That:-

We have Three cards Among them

one is red on both sides.

one is blue on both sides

one is red on one side and blue on their side.

(a) Compute the information content of this observation (that the side facing up is blue.)?

The cards are shuffled ,One card is drawn and that is facing up to blue .

Here, there are 2 chances to get the card facing up is blue they are.

Either both sides blue (or) One side red and One side blue..

Total possibilities =3(i.e., one side is blue , both sides blue no blue.)

Avialiable possibilities = 2(i.e., 1 side blue , 2 sides blue)

Possibility

(b) Find the prior and posterior probability distributions of the color of the bottom side of the card. (Use Bayes’ theorem to calculate the posterior probability distributions.)?

To get the Prior and Posterios probability distribution of the color of the bottom side of the card .using Bayes' theorem as,

P(other side is blue \ side we see is blue)

(c) Find the entropy of each of the probability distributions you calculated in part (a).?

Entropy

orchestra answered 1 year ago

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