Question

Question 1:

part A

Suppose that there are five kinds of bags of candies

• h1: 10% of them are 100% cherry flavor

• h2: 20% of them are 75% cherry flavor and 25% are lime flavor

• h3: 40% of them are 50% cherry flavor and 50% are lime flavor

• h4: 20% of them are 25% cherry flavor and 75% are lime flavor

• h5: 10% of them are 100% lime flavor

We chose a bag of candies and took out 3 candies which were all lime, which is denoted as data d. Compute the following probabilities. (a) P(h1|d) (b) P(h2|d) (c) P(h3|d) (d) P(h4|d) (e) P(h5|d)

part B

Suppose that there is a bag in which cherry flavored candies and lime flavored candies are mixed. When we took out five candies and three of them were cherry flavored ones and two of them were lime flavored ones. What is the most probable value of θ? Explain the reason using maximum likelihood principle.

Answer 1

P13 I ime hom /o w luo /uo 0233 0.237 30 025) O-232r (d) P(hyld) (0-75)3- こ20 0 3553 O-23が