In continuous probability distribution F(x) is called.a)frequency dist...
Continuous Probability Distribution:
Continuous probability distributions are used to model events that can take on any value within a given range. Unlike discrete probability distributions, which are used for events with distinct outcomes, continuous probability distributions represent events with a range of possible outcomes.
Cumulative Distribution Function (CDF):
The cumulative distribution function (CDF) is a function that provides the probability that a random variable takes on a value less than or equal to a given value. It gives the cumulative probability distribution of a random variable.
Explanation:
In the given question, the continuous probability distribution is represented by the function F(x). We need to identify the correct term for this function.
- The frequency distribution function (option A) is used for discrete probability distributions, where it represents the frequency of each outcome in a set of data.
- The probability density function (option C) is used to describe the probability distribution of a continuous random variable. It gives the probability density at each point in the range of the random variable.
- The cumulative distribution function (option B) is the correct answer. It describes the cumulative probabilities of a continuous random variable up to a given value. It gives the probability that the random variable takes on a value less than or equal to a given value.
The cumulative distribution function, F(x), is an important concept in probability theory and statistics. It allows us to calculate probabilities for a continuous random variable by integrating the probability density function over a certain range.
Therefore, the correct answer is option B, the cumulative distribution function (CDF).