Pick a number between 0 and 1. Why is it unlikely that you would pick, say, 0.5495872349857293457293759234579823...?
Assuming a uniform distribution, the probability that you would happen to get the first decimal correct is 1/10. The probability that you would get the second decimal correct is 1/10. And so on. So the probability that you would get all the decimal places correct is 1/10*1/10*1/10*.... which converges to zero. This same argument can be made for any continuous distribution.
Mathematicians have shied away from using the word "impossible" to describe this situation, since we could immagine it possibly happening. The phrase "almost never" is used in conjunction with a probability of zero.
The probability of a random variable being at or below a certain value is defined as the cumulative distribution function (CDF) of the variable. The CDF gives the probability that the variable takes on a value less than or equal to a given value.
Probability density function (PDF) of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a point in the observation space. The PDF is the derivative of the probability distribution (also known as cummulative distriubution function (CDF)) which described the enitre range of values (distrubition) a continuous random variable takes in a domain. The CDF is used to determine the probability a continuous random variable occurs any (measurable) subset of that range. This is performed by integrating the PDF over some range (i.e., taking the area under of CDF curve between two values). NOTE: Over the entire domain the total area under the CDF curve is equal to 1. NOTE: A continuous random variable can take on an infinite number of values. The probability that it will equal a specific value is always zero. eg. Example of CDF of a normal distribution: If test scores are normal distributed with mean 100 and standard deviation 10. The probability a score is between 90 and 110 is: P( 90 < X < 110 ) = P( X < 110 ) - P( X < 90 ) = 0.84 - 0.16 = 0.68. ie. AProximately 68%.
Probability of getting a head or tail is not equal
It is the probability of an event that will definitely happen.
For any particular trial, the total probability is 1.
For a discrete variable, you add together the probabilities of all values of the random variable less than or equal to the specified number. For a continuous variable it the integral of the probability distribution function up to the specified value. Often these values may be calculated or tabulated as cumulative probability distributions.
All other things being equal, 3/4.
It is a probability distribution where when all of the values of a random variable occur with equal probability. Say X is the random variable, such as what number shows up when we roll a die. There are 6 possible outcomes, each with a 1/6 probability of showing up. If we create a probability distribution where X= 1,2,3,4,5, or 6, we note P(X=k)=1/k where k is any number between 1 and 6 in this case. The graph will be a rectangle.
From a probability perspective fair means equal probability.
random sample
From a probability perspective fair means equal probability.
One is the probability, or certain to occur.
The cumulative frequency or the probability of an observed value being less than or equal to a given value. By extension, it would also give the probability of a greater value being observed.
It is a simple random sample.
This is called a random sample.
The probability of an event is the number of outcomes that are favourable to the outcome divided by the total number of outcomes. For continuous variables, it is the proportion of the outcome space, but the same argument applies.The number of favourable outcomes must be non negative and so the probability has to be greater than or equal to 0. Also, the number of favourable outcomes can, at most, be as large as the total number so the probability must be less than or equal to 1.
probability of hitting a white key 7/12, probability of hitting a black key 5/12. Assuming all key have an equal possibility of being hit.