Question
In: Advanced Math
find the stationary distribution of following chain We repeated roll two four sided dice with numbers...
find the stationary distribution of following chain
We repeated roll two four sided dice with numbers 1, 2, 3, and 4 on them. Let Yk be the sum on the kth roll, Sn = Y1 +···+Yn be the total of the first n rolls, and Xn = Sn (mod 6).
Solutions
Colby Messinger answered 12 hours agoRelated Solutions
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the
numbers shown on the dice and Y be the number of dice that show an
odd number.
a) Find the joint pmf of <X,Y>
b) Find the marginals pmf's for both variables.
c) Are X and Y independent?
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the
numbers shown on the dice and Y be the number of dice that show an
odd number.
a) Find the joint pmf of <X,Y>
b) Find the marginals pmf's for both variables.
c) Are X and Y independent?
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on...
Suppose you roll two 6-sided dice, letting X be the sum of the
numbers shown on the dice and Y be the number of dice that show an
odd number.
a) Find the joint pmf of <X,Y>
b) Find the maringals pmf's for both variables.
c) Are X and Y independent?
Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die...
Find the conditional probability, in a single roll of two fair
6-sided dice, that neither die is a
three,given that the sum is greater than 7.
Consider some 8-sided dice. Roll two of these dice. Let X be the minimum of the...
Consider some 8-sided dice. Roll two of these dice. Let X be the
minimum of the two values that appear. Let Y denote the
maximum.
a) Find the joint mass p_X,Y (x,y).
b) Compute p_X│Y (x│y) in all cases. Express your final answer
in terms of a table.
Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum...
Suppose we would roll two standard 6-sided dice.
(a) Compute the expected value of the sum of the rolls.
(b) Compute the variance of the sum of the rolls.
(c) If X represents the maximum value that appears in the two
rolls, what is the expected value of X? What’s the probability of
sum = 7?
Rolling a pair of 12 sided dice and summing the numbers find the following: The probability...
Rolling a pair of 12 sided dice and summing the numbers find the
following:
The probability distribution of the sums.
Sums=
P(Sums)
If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2...
If you roll two six-sided dice, what is the probability of
obtaining the following outcomes?
a)2 or 3
b) 6 and 4
c) At least one 5
d) Two of the same number (two 1s, or two 2s, or two 3s,
etc.)
e) An even number on both dice
f) An even number on at least one die
1. Rolling two D20 Consider what hapens when we roll two 20-sided dice d1 and d2...
1. Rolling two D20
Consider what hapens when we roll two 20-sided dice d1
and d2 (so the sample space is
S={(d1,d2):d1,d2∈{1,2,3,…,20}}
and Pr(ω)=1/|S| for each
ω∈S). Consider the following events:
A is the event "d1=13"
B is the event "d1+d2=15"
C is the event "d1+d2=21"
Use the definitions of independence and conditional probability
to answer these two questions:
Are the events A and B independent?
Are the events A and C independent?
Assume we roll a fair four-sided die marked with 1, 2, 3 and 4. (a) Find...
Assume we roll a fair four-sided die marked with 1, 2, 3 and
4.
(a) Find the probability that the outcome 1 is first observed after
5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are
both observed.
(c) Find the expected number of rolls until the outcome 3 is
observed three times.
(d) Find the probability that the outcome 3 is observed exactly
three times in 10 rolls
given that it is first observed...
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