Question

If $x$ is a continuous random variable then $P(x\ge a)=$

• A. $P(x<a)$
• B. $1-P(x>a)$
• C. $P(x>a)$
• D. $1-P(x\le a-1)$

Answer 1

Answer: (C)

$P(x>a)$

Given $x$ is continuous random variable , Let us consider that there are $n$ points in total, Since $x$ is continuous, $n\to \infty$

The probability of $x=a$ is $\frac{1}{n}\to 0$ , therefore $P(x=a)=0$

Which implies $P(x\ge a)=P(x>a)+P(x=a)=P(x>a)$

Therefore the correct option is $C$