Let X be a continuous random variable A ≤ X ≤ B and let f (x) be its probability density function and F (x) its cumulative distribution function. Indicate whether the following statements are true or false.
-Pr(a ≤ X ≤ b) = $\int _ { a } ^ { b } f ( x ) d x$

Question

Let X be a continuous random variable A ≤ X ≤ B and let f (x) be its probability density function and F (x) its cumulative distribution function.  Indicate whether the following statements are true or false. 
-Pr(a ≤ X ≤ b) = $\int _ { a } ^ { b } f ( x ) d x$

Quizplus · Accepted Answer

The probability that a continuous random variable X falls within the interval [a, b] is given by the integral of its probability density function (pdf) f(x) from a to b, which is exactly what the provided equation represents.

Let X Be a Continuous Random Variable a ≤ X ∫abf(x)dx\int _ { a } ^ { b } f ( x ) d x∫ab​f(x)dx

Let X Be a Continuous Random Variable a ≤ X $\int _ { a } ^ { b } f ( x ) d x$