Branching processes in random environments constitute a significant class of stochastic models designed to capture the interplay between intrinsic reproductive dynamics and extrinsic environmental ...

This is a preview. Log in through your library . Abstract We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the ...

CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

This is a preview. Log in through your library . Abstract In this paper we present novel results for di screte-ti me and Markovian continuous-time multitype branching processes. As a population ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of ...

90 pupils were asked whether they owned a laptop or a tablet device. 52 said they owned a laptop. 45 said they owned a tablet. 23 said they owned both. Find the probability that a pupil chosen at ...

Venn diagrams can be useful for organising information about frequencies and probabilities, which can then be used to solve conditional probability problems. 90 pupils were asked whether they owned a ...