Suppose that one particle can produce a random number of k new particles. Each of the new particles produces another random number of new particles. We assume that the particles act independently of each other and that every particle has a probability pk of producing k new particles (for k = 0, 1, 2, , . . ).

We consider a special case where the outcome of any trial depends on the outcome of the directly preceding trial, and only on it. A stochastic process with this property is referred to as a Markov Chain (or a Markov process).

An absorbing Markov Chain contains only absorbing and transient states. If the number of states is finite, a Markov process starting from any transient state will eventually end in one of the absorbing states. Suppose that there are s absorbing states and t transient states so that the transition matrix P is order (s + t).

In this Chapter, we develop probability models for some special cases of birth-and –death process involving the population size within a given system at time t. The probability generating function can be used to analyze the process in the case where the actual probability distribution cannot be obtained. We also obtain deterministic models corresponding to the given probability models.

This course will provide you with an introduction to the sociology of work. It is designed to provide you with a broad overview while giving emphasis to specific topics in detail. It is beyond the scope of this unit to cover the field of work and industry in entirety.

Given adequate and focussed preparation, this kit should be useful in enabling any student preparing for examinations in Auditing and related courses to pass with good grades in the exams.

Initially psychology was a branch of philosophy that explained human nature from metaphysical (unscientific) perspective. For example, with this definition a parent would say that his child is not doing well in class because he is being cursed. Yet a more realistic explanation could be from a variety of sources such as social problems and poor teaching methods. The word psychology was derived from two Greek words (1 ) psyche - mind, soul, spirit and (2) logos - the study of-----. Therefore, psychology was initially defined as "The study of the mind

Education promotes international consciousness and foster positive attitudes towards other nations Kenya is part of the interdependent network of diverse peoples and nations. Education should empower the learner to respect, appreciate and participate in the opportunities within the international community. Education should also enable the learner to operate within the international community with full knowledge of the obligations, responsibilities, rights and benefits that this membership entails

Speaking or oral communication can be defined as: An interactive process of constructing meaning that involves producing, receiving and processing information (Brown, 1994; Burns & Joyce, 1997). Speaking means to converse, or expressing one's thoughts and feelings in spoken language. This could be an informal remark, scholarly presentation or a formal address. Speaking skills are the skills that give us the ability to communicate effectively. These skills allow the speaker, to convey his message in a passionate, thoughtful, and convincing manner. Speaking skills also help to assure that one won't be misunderstood by those who are listening. The form and meaning of speaking are dependent on the context in which it occurs, thus Oral communication cannot occur in a vacuum

An object attached to a coil spring can exhibit oscillatory motion. Many kinds of oscillatory motion are sinusoidal in time, or nearly so, and are referred to as simple harmonic motion. Real systems generally have at least some friction, causing the motion to be damped. The automobile spring shown here has a shock absorber (yellow) that purposefully dampens the oscillation to make for a smooth ride. When an external sinusoidal force is exerted on a system able to oscillate, resonance occurs if the driving force is at or near the natural frequency of oscillation.