Question

In: Statistics and Probability

4. Recall the cookie problem from lecture. We have two bowls, Bowl 1 and Bowl 2....

4. Recall the cookie problem from lecture. We have two bowls, Bowl 1 and Bowl 2. Bowl 1 contains 25% chocolate and 75% vanilla cookies; Bowl 2 has 50% of each. For this problem, assume each bowl is large enough that drawing a single cookie does not appreciably alter this ratio. Suppose we draw two cookies from the bowl and they are both chocolate. Calculate the posterior probabilities of the two bowls in two ways: (a) by treating the two cookies as one simultaneous piece of evidence (b) by updating the prior probabilities once using the rst chocolate cookie, and using the posterior probabilities as prior probabilities in a second update.

5. Suppose instead we draw two cookies; one is chocolate and the other is vanilla. Calculate the posterior probabilities. Does it matter which cookie we drew rst? Why or why not?

please answer this two question

Solutions

Expert Solution

Solution:

orchestra answered 1 year ago
Next > < Previous

Related Solutions

We have 3 bowls, 1) The first bowl contains 3 red and 2 green balls 2)...
We have 3 bowls, 1) The first bowl contains 3 red and 2 green balls 2) the second bowl contains 2 red and 1 white balls 3) the third one contains 1 red and 3 green balls One bowl by the random is selected and then 2 balls will be drawn. what is the probability that both of these balls will be red?
We have 3 bowls, 1) The first bowl contains 3 red and 2 green balls 2)...
We have 3 bowls, 1) The first bowl contains 3 red and 2 green balls 2) the second bowl contains 2 red and 1 white balls 3) the third one contains 1 red and 3 green balls One bowl by the random is selected and then 2 balls will be drawn. what is the probability that both of these balls will be red?
We have 3 bowls, 1) The first bowl contains 3 red and 2 green balls 2)...
We have 3 bowls, 1) The first bowl contains 3 red and 2 green balls 2) the second bowl contains 2 red and 1 white balls 3) the third one contains 1 red and 3 green balls One bowl by the random is selected and then 2 balls will be drawn. what is the probability that both of these balls will be red?
: Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company...
: Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has 8 adjacent positions on its Boeing-727 aircraft for freight containers. The weights of this containers depend on what they are carrying. and company statistics indicate that %7 of the containers are classified as ”heavy”. While heavy containers are not inherently dangerous, having two such containers next to each other is considered dangerous should the plane encounter a wind gust. Understandably, company wants to...
Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has...
Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has 8 adjacent positions on its Boeing-727 aircraft for freight containers. The weights of this containers depend on what they are carrying. and company statistics indicate that %7 of the containers are classified as ”heavy”. While heavy containers are not inherently dangerous, having two such containers next to each other is considered dangerous should the plane encounter a wind gust. Understandably, company wants to know...
Bowl 1 contains 7 red and 3 white chips. Bowl 2 contains 4 red and 5...
Bowl 1 contains 7 red and 3 white chips. Bowl 2 contains 4 red and 5 white chips. A chip is randomly selected from Bowl 1 and placed in Bowl 2, then two chips are drawn from Bowl 2 without replacement. Find the probability that both chips drawn from Bowl 2 are red.
Background: Recall from the lecture notes that an integer x can be represented as a vector...
Background: Recall from the lecture notes that an integer x can be represented as a vector [xw−1, xw−2, . . . , x0], where w is the number of bits used to represent x. As a fun exercise, let us consider a problem where we want to partition x into two new numbers, labelled y and z. We can do this by scanning through the bits of x from the least significant bit (lsb) to the most significant bit (msb)....
Consider the problem from Lecture 4, “Search, Sampling and Independence.” Assume that the distribution of prices...
Consider the problem from Lecture 4, “Search, Sampling and Independence.” Assume that the distribution of prices from which the consumer draws is (i) discrete and (ii) Uniformly distributed with N possible stores/prices from which to draw. (a) If the consumer is lost in the mall and doesn’t remember the last store he visited (i.e. the last price he drew) and so cannot avoid the possibility of returning to the same store, are successive price draws dependent or independent? (b) If...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall) gives a contest a chance to choose from three doors of which one is a new car and the other two are goats. After the contestant chooses a door, the game show host who knows what is behind all of the doors decides to open another door behind which a goat sits. The games show host. then, offers the contestant an opportunity to switch...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall) gives a contest a chance to choose from three doors of which one is a new car and the other two are goats. After the contestant chooses a door, the game show host who knows what is behind all of the doors decides to open another door behind which a goat sits. The games show host. then, offers the contestant an opportunity to switch...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT