Random experiment

For example, consider Uie random experiment of drawing two cards in succession from a deck of 52 cards. Suppose Uie cards are drawn wiUiout replacement (i.e., Uie first card drawn is not replaced before the second is drawn). Let A denote Uie event Uiat Uie first card is an ace and B Uie event Uiat Uie second card is an ace. The sample space S can be described as a set of 52 times 51 pairs of cards. Assuming Uiat each of these (52)(51) pairs lias Uie same Uieoretical relative frequency, assign probability 1/(52)(51) to each pair. The number of pairs featuring an ace as Uie first and second card is (4)(3). Therefore,... 

A random variable is a real-valued function defined over tlie sample space S of a random experiment (Note tliat tliis application of probability tlieorem to plant and equipment failures, i.e., accidents, requires tliat tlie failure occurs randomly. 

Probabilities are nonnegative nmnbers associated with the outcomes of so-called random experiments. A random experiment is an experiment whose outcome is uncertain. 

Consider n independent performances of a random experiment witli mutually exclusive outcomes that can be classified "success or failure . Tlie words success and failure are to be regarded as labels for two mutually exclusive categories of outcomes of the random experiment. They do not necessarily have tlie ordinary connotations of success or failure. Assume tliat p, tlie probability... 

The probability distribution of X, tlie number of successes in n performances of tlie random experiment, is tlie binomial distribution, witli pdf specified by... 

A quantity that appears in a random experiment. Random variables relate events into a set of values. 

Manning, W.G. et al. (1987), Health insurance and the demand for medical care evidence from a randomized experiment , American Economic Review, 11,251-77. 

The importance of the strength of tt complex adsorption on the reaction rate through the operation of displacement effects is further demonstrated by naphthalene randomization reactions. Naphthalene exchanges very slowly with deuterium oxide. That this is due to the displacement of water by normal naphthalene and not due to a toxic side reaction, such as polymerization, is shown in randomization experiments with mono a-deuterated naphthalene. Randomization is completed within 24 hours at 120°, whereas no significant deuteration occurs under the same reaction conditions with water. This result furnishes additional proof for the dissociative exchange mechanism. 

Buyse M, Molenberghs G. Criteria for the validation of surrogate endpoints in randomized experiments. Biometrics 1998 54 1014-29. 

Molenberghs G, Geys H, Buyse M. Evaluation of surrogate endpoints in randomized experiments with mixed discrete and continuous outcomes. Stat Med 2001 20 3023-38. 

An experiment that can result in different outcomes, even though the experiment is repeated by exactly the same procedure every time. A random variable is a numerical outcome of a random experiment. See Statistics (A Primer)... 

A statistical term for the list or set (denoted as S) of all possible outcomes of a random experiment. In the case of a perfectly balanced, infinitely thin coin, there are only two outcomes, Heads and Tails, in the sample space. See Random Experiment Statistics (A Primer)... 

For the tablet formulation example of Table 2.1, this split-plot arrangement would require mxnxl = 9x8 = 72 tablet formulation batches to be made but only mxl = 9 operations of the climate chamber. The experiment would be conducted by placing in the climate chamber a complete set of 8 different tablet formulations at the same time. A completely randomized experiment (the cross-product experiment of... 

Perform randomized experiments according to statistical model Calculate effects of each factor and test for statistical significance... 

In all these above statements we have tried to express the chances of Amit for standing first in his class qualitatively. This is an event which may and may not happen. But we are predicting the result of the event with some uncertainty. This uncertainty associated with the event may be lesser or greater, i.e., it may vary. In mathematics we measure, this uncertainty in terms of number quantitatively which we call probability or chance. With the help of probability we can predict the outcome of any random experiment by associating some probability to that outcome. 

It should be noted that the control conditions of Roberts and Phelps eliminated both temporal serial order cues and spatial cues, since problems were presented concurrently and their spatial positions were either randomized (Experiment 1) or placed in a circle (Experiment 2). When both sources of ordering were removed, animals showed indifference between stimuli B and D. Could rats use just serial order as a cue Davis (1992) trained rats with no spatial cues present but presented his training pairs in serial order. When tested, rats showed significant transitive inference. This finding, when combined with that of Roberts and Phelps, suggests that rats can use either spatial order or temporal order as a cue for the overall order of training stimuli. What is unknown from these observations is whether the final representations differ or are the same. That is, could a rat use temporal order to form a spatial representation of linearity or use spatial position to form a temporal representation of linearity Such questions await further research. 

Defining a random variable on a sample space S amounts to coding tlie outcomes in real numbers. Consider, for example, the random experiment involving die selection of an item at randoni from a manufactured lot. Associate X = 0 widi die drawing of a non-defective item and X = 1 widi die drawing of a defective item. Tlien X is a randoni variable with range (0, 1) and dierefore discrete. 

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