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Why the probability of a continuous variable being equal to an exact value is zero?
Wiki User
∙ 11y ago
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.
Wiki User
∙ 11y ago
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How often the value of a random variable is at or below a certain value.?
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.
What is the difference between probability distribution functions and probability density functions?
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%.
What is a biased coin in probability?
Probability of getting a head or tail is not equal
What is the event if the probability will equal 1?
It is the probability of an event that will definitely happen.
What is a variable divided by the coefficient that will equal 7?
Any variable divided by coefficients can equal 7 - provided the variable can take the appropriate value.
How do calculate the probability of at most?
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.
Is the total area within a continuous probability distribution is equal to 1?
Yes.
How often the value of a random variable is at or below a certain value.?
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.
What is the difference between probability distribution functions and probability density functions?
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%.
What is the probability that a Poisson random variable x is equal to 5...?
It depends on the parameter - the mean of the distribution.
Is the total area within any continuous probability distribution is equal to 1.00?
Yes, but not just continuous prob distribs. It applies to discontinous or discrete distributions as well.
Difference between variables and probability distribution?
Assuming you mean random variable here. A random variable is term that can take have different values. for example a random variable x that represent the out come of rolling a dice, that is x can equal 1,2,3,4,5,or 6. Think of probability distribution as the mapping of likelihood of the out comes from an experiment. In the dice case, the probability distribution will tell you that there 1/6 the time you will get 1, 2,3....,or 6. this is called uniform distribution since all the out comes have that same probability of occurring.
What is the probability that the card is not a heart?
All other things being equal, 3/4.
What is a uniform probability distribution?
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.
What is the difference between discrete and cumulative distributions?
A discrete distribution is one in which the random variable can take only a limited number of values. A cumulative distribution, which can be discrete of continuous, is the sum (if discrete) or integral (if continuous) of the probabilities of all events for which the random variable is less than or equal to the given value.
When do you use uniform distribution?
When, over a given range, the probability that a variable in question lies within a particulat interval is equal to the size of that interval as a proportion of the range.
Two equal sized flasks are connected with one molecule inside what is the probability that the molecule will be in flask A What is the probability it will be in flask B?
There should be equal probability (at least over time) of the molecule being in either flask (as long as you don't have to account for the possibility of it being in a region connecting the two flasks but belonging to neither). Thus the probability is 50% it's in A and 50% it's in B.
