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A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.

Q: What is the difference between probability distribution and probability density function?

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None. The full name is the Probability Distribution Function (pdf).

They are the same. The full name is the Probability Distribution Function (pdf).

what is density curve

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.

The normal distribution is a continuous probability distribution that describes the distribution of real-valued random variables that are distributed around some mean value.The Poisson distribution is a discrete probability distribution that describes the distribution of the number of events that occur within repeated fixed time intervals, where the mean frequency is a known value, and each interval is independent of the prior interval(s)/event(s).

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None. The full name is the Probability Distribution Function (pdf).

They are the same. The full name is the Probability Distribution Function (pdf).

what is density curve

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 probability mass function is used to characterize the distribution of discrete random variables, while the probability density function is used to characterize the distribution of absolutely continuous random variables. You might want to read more about this at www.statlect.com/prbdst1.htm (see the link below or on the right)

Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.

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The skew binomial distribution arises when the probability of a particular event is not a half.

The uniform distribution is limited to a finite domain, the normal is not.

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.

A probability density function (pdf) for a continuous random variable (RV), is a function that describes the probability that the RV random variable will fall within a range of values. The probability of the RV falling between two values is the integral of the relevant PDF. The normal or Gaussian distribution is one of the most common distributions in probability theory. Whatever the underlying distribution of a RV, the average of a set of independent observations for that RV will by approximately Gaussian.

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.