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No. The probability that a continuous random variable takes a specific value is always zero.

Q: Does the probability that a continuous random variable take a specific value depend on the probability density function?

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Yes.

It depends on what the random variable is, what its domain is, what its probability distribution function is. The probability that a randomly selected random variable has a value between 40 and 60 is probably quite close to zero.

The probability of scoring an exact value for a continuous variable is zero for any value. The probability of scoring 115 (or more) is 15.87%

It is a continuous variable.

yes

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It is a function which is usually used with continuous distributions, to give the probability associated with different values of the variable.

Zero.

The formula, if any, depends on the probability distribution function for the variable. In the case of a discrete variable, X, this defines the probability that X = x. For a continuous variable, the probability density function is a continuous function, f(x), such that Pr(a < X < b) is the area under the function f, between a and b (or the definite integral or f, with respect to x, between a and b.

You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.

Yes. It is a continuous variable. As used in probability theory, it is an example of a continuous random variable.

I am not quite sure what you are asking. If this answer is not complete, please be more specific. There are many probability density functions (pdf) of continuous variables, including the Normal, exponential, gamma, beta, log normal and Pareto. There are many links on the internet. I felt that the related link gives a very "common sense" approach to understanding pdf's and their relationship to probability of events. As explained in the video, a probability can be read directly from a discrete distribution (called a probability mass function) but in the case of a continuous variable, it is the area under the curve that represents probability.

A random variable is a variable that can take different values according to a process, at least part of which is random.For a discrete random variable (RV), a probability distribution is a function that assigns, to each value of the RV, the probability that the RV takes that value.The probability of a continuous RV taking any specificvalue is always 0 and the distribution is a density function such that the probability of the RV taking a value between x and y is the area under the distribution function between x and y.

The integral of the density function from the given point upwards.

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.

A discrete random variable (RV) can only take a selected number of values whereas a continuous rv can take infinitely many.

There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.

There are infinitely many continuous probability functions and there is no information whatsoever in the question to determine the nature of the distribution: uniform, Normal, Student's t, Chi-square, Fisher's F, Gamma, Beta, Lognormal, etc, etc. Second, every continuous function must have at least two points for which the probability is the same. There is no information as to which of these two (or more) points is the relevant one. There can therefore be no answer.