The __________ distribution has the following equations:

Question

BlackTom AI · Accepted Answer

The question states: 'The __________ distribution has the following equations:' and provides the variance formula Var(X) = σ^2 = (b − a)^2 / 12. This specific variance expression is a hallmark of the Uniform distribution on the interval [a, b], whose standard result is Var(X) = (b − a)^2 / 12. In contrast, many other common distributions have different variance formulas that depend on other parameters (for example, Normal distributions involve variance σ^2 not in the (b−a) form, and Exponential/Geometric have variances tied to rate parameters rather than an interval width). Therefore, the variance equation given aligns with a Uniform distribution over [a, b].

Since the answer options are not provided here, there is no direct alternative to compare within the list. However, understanding that (b − a)^2 / 12 is the variance for Uniform(a, b) helps identify the blank as referring to the Uniform distribution. Keep in mind that if other distributions were listed, you would compare their standard variance expressions to see which one matches (b − a)^2 / 12, anditis unlikely to match for distributions that do not have a finite support width parameterized by a and b in the same way.

In summary, recognizing that the interval width (b − a) governs the spread for a Uniform distribution explains why its variance takes the form (b − a)^2 / 12, distinguishing it from other common distributions' variance formulas.

ECON 3640-090 Spring 2025 Lecture #16 Warm-Up

The __________ distribution has the following equations:

查看解析

登录即可查看完整答案

类似问题

Question at position 1 The shape of the uniform probability distribution is:positively skewed.negatively skewed.bell-shaped.rectangular

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in less than 6 minutes is

Which one of these images shows data generated uniformly at random?

The height of the probability density function f(x) of a random variable X that is uniformly distributed between a and b is:

If the random variable X is uniformly distributed between 40 and 60, then P(35 ≤ X ≤ 45) is:

A computer program generates a random number to simulate a user's reaction time, which is known to lie between 200 and 500 milliseconds, with all values in that range equally likely.Which probability distribution is most appropriate for modeling the reaction time?

Students’ arrivals at Insearch follow a uniform distribution from 9 am to 2 pm. Let x be the time that students arrive at Insearch. What is the probability that students arrive between 10 am and 11 am? Provide the answer as a fraction to one decimal place.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单