Random Walk on a number line and further cases
$begingroup$
i)
A monkey is sitting on 0 on the real line in period 0. In every period t ∈ {0, 1, 2, . . .} it moves 1 to the right with probability p and 1 to the left with probability 1−p, where p ∈ 1 2 , 1 . Let πk denote the probability that the monkey will reach positive integer k in some period t > 0. The value of πk for any positive integer k is
A)p
B)1
C)0
D)p/1-p
ii)
Refer to the previous question. Suppose p = 1/2
and πk
denote the probability that the monkey will reach positive
integer k in some period t > 0. The value of π0 is
(a) 0
(b) 1/2^k
(c) 1/2
(d) 1
The answer key says the answer to both of them is 1. What is the possible mathematical explanation and also the intuition?
random-walk gambling
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
$endgroup$
add a comment |
$begingroup$
i)
A monkey is sitting on 0 on the real line in period 0. In every period t ∈ {0, 1, 2, . . .} it moves 1 to the right with probability p and 1 to the left with probability 1−p, where p ∈ 1 2 , 1 . Let πk denote the probability that the monkey will reach positive integer k in some period t > 0. The value of πk for any positive integer k is
A)p
B)1
C)0
D)p/1-p
ii)
Refer to the previous question. Suppose p = 1/2
and πk
denote the probability that the monkey will reach positive
integer k in some period t > 0. The value of π0 is
(a) 0
(b) 1/2^k
(c) 1/2
(d) 1
The answer key says the answer to both of them is 1. What is the possible mathematical explanation and also the intuition?
random-walk gambling
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
$endgroup$
add a comment |
$begingroup$
i)
A monkey is sitting on 0 on the real line in period 0. In every period t ∈ {0, 1, 2, . . .} it moves 1 to the right with probability p and 1 to the left with probability 1−p, where p ∈ 1 2 , 1 . Let πk denote the probability that the monkey will reach positive integer k in some period t > 0. The value of πk for any positive integer k is
A)p
B)1
C)0
D)p/1-p
ii)
Refer to the previous question. Suppose p = 1/2
and πk
denote the probability that the monkey will reach positive
integer k in some period t > 0. The value of π0 is
(a) 0
(b) 1/2^k
(c) 1/2
(d) 1
The answer key says the answer to both of them is 1. What is the possible mathematical explanation and also the intuition?
random-walk gambling
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
$endgroup$
i)
A monkey is sitting on 0 on the real line in period 0. In every period t ∈ {0, 1, 2, . . .} it moves 1 to the right with probability p and 1 to the left with probability 1−p, where p ∈ 1 2 , 1 . Let πk denote the probability that the monkey will reach positive integer k in some period t > 0. The value of πk for any positive integer k is
A)p
B)1
C)0
D)p/1-p
ii)
Refer to the previous question. Suppose p = 1/2
and πk
denote the probability that the monkey will reach positive
integer k in some period t > 0. The value of π0 is
(a) 0
(b) 1/2^k
(c) 1/2
(d) 1
The answer key says the answer to both of them is 1. What is the possible mathematical explanation and also the intuition?
random-walk gambling
random-walk gambling
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
asked Dec 24 '18 at 8:14
Vasu VikramVasu Vikram
11
11
add a comment |
add a comment |
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