Question 22

Mathematics Probability Easy

Cumulative Density Function \( \mathrm{F}(\mathrm{x}) \) of a continuous random variable X is defined as:

(A) \( F(x)=\int_{-\infty}^{x} f(x) d x \)
(B) \( F(x)=\int_{1}^{x} f(x) d x \)
(C) \( F(x)=\int_{-\infty}^{\infty} f(x) d x \)
(D) \( F(x)=P[X=x] \)
✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The cumulative distribution function gives the probability that X takes a value up to \(x\):

\(F(x) = P(X \le x) = \int_{-\infty}^{x} f(t)\,dt\)

where \(f\) is the probability density function.

Option (C) always equals 1, and (D) is always 0 for a continuous variable.

Answer: (A)

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