Correct option is B
Poisson distribution: The Poisson distribution is a discrete probability distribution that represents the number of events occurring within a fixed interval of time or space, assuming the events happen at a constant average rate and are independent of each other. In the Poisson distribution, both the mean and variance are equal to the parameter (which represents the average rate of occurrences).
The mean and variance are equal (both λ). The distribution is used to model count data, such as the number of times an event occurs in a given time period.
Additional Knowledge
Gaussian distribution: The Gaussian is a continuous probability distribution that is symmetric about the mean, with its shape forming a bell curve. The mean (µ) determines the center of the distribution, and the variance (σ2) determines the spread or width of the curve. In this distribution, the mean and variance are independent parameters, so they can take different values.
The total area under the curve equals 1, and the distribution is symmetric around the mean. The variance affects the width of the bell curve.
Exponential distribution: The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, where the events occur continuously and independently at a constant average rate.
The mean of the exponential distribution is 1/ λ, and the variance is 1/ λ2 , where λ is the rate parameter. Since the mean and variance have different formulas, they are not equal.
This distribution is often used to model waiting times, such as the time until the next event in a Poisson process.
Uniform distribution: The uniform distribution is a continuous probability distribution where all outcomes are equally likely within a given range [a, b]. The mean of a uniform distribution is (a + b)/2, and the variance is (b - a)2/12, which means the mean and variance depend on the range of the distribution. All intervals of the same length within the range have the same probability, and the mean and variance are not equal.
