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What is the law of large numbers and how does it pertain to empirical probability?
Wiki User
∙ 11y ago
well the law of large numbers is A therom that describes the result of performing the same experiment a large number of times and its like empirical because its like actually experimenting it or something like that .
Wiki User
∙ 11y ago
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Why did Mendel study such a large sample of pea plants to determine the probability of inheritance?
The more samples you use, the closer your results will match probability.
What shape would the probability distribution have for completely uncertain returns?
the variance is infinitely large and in the extreme case the probability distribution curve will simply be a horizontal line
How do you calculate experimental probability?
Experimental probability is the number of times some particular outcome occurred divided by the number of trials conducted. For instance, if you threw a coin ten times and got heads seven times, you could say that the experimental probability of heads was 0.7. Contrast this with theoretical probability, which is the (infinitely) long term probability that something will happen a certain way. The theoretical probability of throwing heads on a fair coin, for instance, is 0.5, but the experimental probability will only come close to that if you conduct a large number of trials.
How does a large sample size help to ensure that experimental results are reliable?
It made his actual results approach the results predicted by probability
What is the probability that a randomly chosen number is not divisible by 2 3 or 6?
AnswerThe probability that a randomly chosen [counting] number is not divisible by 2 is (1-1/2) or 0.5. One out of two numbers is divisible by two, so 1-1/2 are not divisible by two.The probability that a randomly chosen [counting] number is not divisible by 3 is (1-1/3) = 2/3.Similarly, the probability that a randomly chosen [counting] number is not divisible by N is (1-1/N).The probability that a random number is not divisible by any of 2, 3 or 6 can be reduced to whether it is divisible by 2 or 3 (since any number divisible by 6 can definitely be divided by both and so it is irrelevant). This probability depends on the range of numbers available. For example, if the range is all whole numbers from 0 to 10 inclusive, the probability is 3/11, because only the integers 1, 5, and 7 in this range are not divisible by 2, 3, or 6. If the range is shortened, say just from 0 to 1, the probability is 1/2.Usually questions of this sort invite you to contemplate what happens as the sampling range gets bigger and bigger. For a very large range (consisting of all integers between two values), about half the numbers are divisible by two and half are not. Of those that are not, only about one third are divisible by 3; the other two-thirds are not. That leaves 2/3 * 1/2 = 1/3 of them all. As already remarked, a number not divisible by two and not divisible by three cannot be divisible by six, so we're done: the limiting probability equals 1/3. (This argument can be made rigorous by showing that the probability differs from 1/3 by an amount that is bounded by the reciprocal of the length of the range from which you are sampling. As the length grows arbitrarily large, its reciprocal goes to zero.)This is an example of the use of the inclusion-exclusion formula, which relates the probabilities of four events A, B, (AandB), and (AorB). It goes like this:P(AorB) = P(A) + P(B) - P(AandB)In this example, A is the event "divisible by 2", and B is the event "divisible by 3".
What is the empirical probability of tossing a coin 5 times and obtaining at least 3 consecutive heads?
The empirical probability can only be determined by carrying out the experiment a very large number of times. Otherwise it would be the theoretical probability.
What is law of large numbers?
when a probability experiment is repeated a large number of times, the relative frequency probability of an outcome will approach its theoretical probability.
How can you use simulations to estimate probability?
Experimental or empirical probability is estimated from repeated trials of an experiment. However, instead of actually carrying out the experiment a very large number of times, it may be possible to simulate them.
The law of large numbers?
The law of large numbers states that as the number of observations in a sample increases, the sample mean will tend to approach the population mean. In other words, the larger the sample size, the more accurate the estimate of the population parameter. This law forms the basis for statistical inference and hypothesis testing.
How is math related to accounting?
Math is related to accounting because they both pertain to numbers. Accounting deals with money amounts, which is a large part of math.
How do you use probability to help humankind?
there is a large probability that mankind will come to an end
What is the theoretical probability of rolling a number that is a multiple of 2 and a 6 sided die?
ans2. The probability of an even number resulting; from a large number of throws; would be 1/2. For 1/2 of the numbers 1 - 6 are even.
What are theoretical and expierimental probability?
Theoretical probability is the probability of something occurring when the math is done out on paper or 'in theory' such as the chance of rolling a six sided dice and getting a 2 is 1/6. Experimental probability is what actually occurs during an experiment trying to determine the probability of something. If a six sided dice is rolled ten times and the results are as follows 5,2,6,2,5,3,1,4,6,1 then the probability of rolling a 2 is 1/3. The law of large numbers states the more a probability experiment is preformed the closer to the theoretical probability the results will be.
What must you know about a data set before you can use the empirical rule?
The data set must be unbiased, the outcomes of the trials leading to the data set must be independent. The data set must be large enough to allow the Law of Large Numbers to be effective.
What is the theoretical probability for getting an odd product?
The theoretical probability of getting an odd product would depend on the specific scenario. If we are talking about rolling a pair of fair dice, the probability would be 1/2 since half of the possible outcomes (3, 5, 15, etc.) would result in an odd product. However, if we are talking about multiplying two randomly selected numbers from a large set, the probability would depend on the distribution of the numbers in the set.
What are names of large numbers?
Obviously "large numbers"
How do you find experimental-probability?
To find the experimental probability of an event you carry out an experiment or trial a very large number of times. The experimental probability is the proportion of these in which the event occurs.
