1. There are two boxes, each of which contains a certain number of cubes and balls, painted in either red or blue. The numbers of different kinds of cubes and balls in both boxes are given by the following table: Вох 1 Box 2 red | blue red | blue 6 24 14 56 cube 28 42 ball 12 18 A person first flips a fair coin. If the coin show a head, he will draw an item from Box 1, otherwise draw an item from Box 2. Let's define the following random variables: if the coin shows a head B 0 if the coin showy a tail

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1. There are two boxes, each of which contains a certain mumber of cubes and balls, painted in
either red or blue. The numbers of different kinds of cubes and balls in both boxes are given
by the following table:
Воx 1
Вох 2
red | blue red | blue
cube
6
24
28
42
ball
14
56
12
18
A person first flips a fair coin. If the coin show a head, he will draw an item from Box 1,
otherwise draw an item from Box 2. Let's define the following random variables:
1 if the coin shows a head
0 if the coin shows a tail
| 1 if the item is a cube
0 if the item is a ball
1 if the item is red
0 if the item is blue
B
%3D
Answer the following questions:
(a) Find the joint PMF of (S, C).
(b) Find the conditional PMF of S given C = 1.
Transcribed Image Text:1. There are two boxes, each of which contains a certain mumber of cubes and balls, painted in either red or blue. The numbers of different kinds of cubes and balls in both boxes are given by the following table: Воx 1 Вох 2 red | blue red | blue cube 6 24 28 42 ball 14 56 12 18 A person first flips a fair coin. If the coin show a head, he will draw an item from Box 1, otherwise draw an item from Box 2. Let's define the following random variables: 1 if the coin shows a head 0 if the coin shows a tail | 1 if the item is a cube 0 if the item is a ball 1 if the item is red 0 if the item is blue B %3D Answer the following questions: (a) Find the joint PMF of (S, C). (b) Find the conditional PMF of S given C = 1.
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