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Results tagged with Search options user 14836

A stochastic process with the property that the future is conditionally independent of the past, given the present.

1
vote
2answers
I found the following definition: "A probabilitly distribution $\pi = \{\pi_x\}_{x \in S}$ on the state space $S$ is called a stationary distribution for the Markov chain if for every $t > 0$, $$ \p …
asked Nov 22 '12 by Kaish
19
votes
3answers
I'm doing a question on Markov chains and the last two parts say this: Does this Markov chain possess a limiting distribution. If your answer is "yes", find the limiting distribution. If your a …
asked Jan 22 '13 by Kaish
1
vote
0answers
The lifetime of a machine is modelled by an exponential random variable $X$ with $P(X>x) = e^{-\lambda x}, \lambda, x > 0$. This machine cannot be repaired. A maintenance crew checks this machine a …
asked Jan 21 '13 by Kaish
1
vote
3answers
I don't understand what the answers say The transition matrix is $$ \begin{pmatrix} 0.5 & 0.5 & 0 \\ 0 & 0.5 & 0.5\\ 0 & 0 & 1 \end{pmatrix} $$ In the answers it says: $C_1 = \{3\}, T = \{1,2\}$, …
asked Dec 15 '12 by Kaish
0
votes
1answer
A newspaper uses one ton of newsprint every day. It buys its newsprint from a local distributor. This ditributor supplies the newsprint in one-ton rolls at the cheapest price, but unfortunatley its …
asked Jan 24 '13 by Kaish
0
votes
0answers
If $Q$ is a generator matrix of a continuous time Markov chain (CTMC), and I need to use this matrix to solve the Kolmogorov forward equation, I would need to start by integrating it. But I haven't go …
asked Jan 8 '13 by Kaish
2
votes
2answers
Suppose that the chain is intitially in state $1$, i.e $P(X_0 = 1) = 1$. Let $\tau$ denote the time of first return to state $1$, i.e $$\tau = \min\{n > 0: X_N = 1\}.$$ Show that $$ …
asked Jan 21 '13 by Kaish
3
votes
1answer
I have the one step transition matrix $$\pmatrix{0 & \alpha & 0 & \beta \\ \alpha & 0 & \beta & 0 \\ 0 & \beta & 0 & \alpha \\ \beta & 0 & \alpha & 0 \\}$$ I want to work out the stationary distribu …
asked Jan 24 '13 by Kaish
1
vote
0answers
Suppose the weather condition classified as "sunny" (S) or "rainy" (R). Assume the condition on day $n + 1$ is dependent on the days $n$ and $n-1$ only. Work out the transition matrix from the tabl …
asked Jan 20 '13 by Kaish
2
votes
2answers
Two containers $A$ and $B$ are placed adjacently to each other and gas passes through a small aperture joining them. A total of $N(>1)$ molecules is distributed among the containers. Ass …
asked Jan 20 '13 by Kaish
4
votes
1answer
Let $\lambda \mu > 0$ and let $X$ be a Markov chain on $\{1,2\}$ with generators $$ Q = \begin{pmatrix} -\mu & \mu \\ \lambda & -\lambda \end{pmatrix}$$ Write down the forward equations and solve th …
asked Dec 21 '12 by Kaish
4
votes
2answers
"Let $\{X_n, n \geq 0\}$ be a DTMC with state space $S = \{1, 2, 3, 4, 5\}$ and the following transition probability matrix: $$ P = \begin{pmatrix} 0.1 & 0.0 & 0.2 & 0.3 & 0.4 \\ 0.0 & 0.6 & 0.0 & 0. …
asked Dec 14 '12 by Kaish