An individual named Claudius is located at the point 0 in the accompanying diagram. A2 B2 A3 B1 0, B3 A1 B4 A4 Using an appropriate randomization device (such as a tetrahedral die, one having four sides), Claudius first moves to one of the four locations B,, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius next returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one of the (new) adjacent points is determined by tossing an appropriate die or coin. (a) Let X = the number of moves that Claudius makes before first returning to 0. What are possible values of X? О 2, 3, 4, .. 2, 4, 6, ... (1, c0) [2, co0) Is X discrete or continuous? discrete continuous (b) If moves are allowed also along the diagonal paths connecting 0 to A,, A,, Az, and A, respectively, what are possible values of X? О 2, 3, 4, ... 2, 4, 6, (1, c0) [2, co) Is X discrete or continuous? discrete continuous
An individual named Claudius is located at the point 0 in the accompanying diagram. A2 B2 A3 B1 0, B3 A1 B4 A4 Using an appropriate randomization device (such as a tetrahedral die, one having four sides), Claudius first moves to one of the four locations B,, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius next returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one of the (new) adjacent points is determined by tossing an appropriate die or coin. (a) Let X = the number of moves that Claudius makes before first returning to 0. What are possible values of X? О 2, 3, 4, .. 2, 4, 6, ... (1, c0) [2, co0) Is X discrete or continuous? discrete continuous (b) If moves are allowed also along the diagonal paths connecting 0 to A,, A,, Az, and A, respectively, what are possible values of X? О 2, 3, 4, ... 2, 4, 6, (1, c0) [2, co) Is X discrete or continuous? discrete continuous
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:An individual named Claudius is located at the point 0 in the accompanying diagram.
A2
B2
A3
B1
0,
B3
A1
B4
A4
Using an appropriate randomization device (such as a tetrahedral die, one having four sides), Claudius first moves to one of the four
locations B,, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius next
returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one
of the (new) adjacent points is determined by tossing an appropriate die or coin.
(a) Let X = the number of moves that Claudius makes before first returning to 0. What are possible values of X?
О 2, 3, 4, ...
2, 4, 6, ...
(1, 00)
[2, 00)
Is X discrete or continuous?
discrete
continuous
(b) If moves are allowed also along the diagonal paths connecting 0 to A,, A,, Az, and A, respectively, what are possible values of
X?
О 2, 3, 4, ...
2, 4, 6,
...
(1, c0)
[2, co)
Is X discrete or continuous?
discrete
continuous
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