Question

f(x) is the probability density function of a continuous random variable X. Then

Answer 1

Final Answer: 1

Steps:
1) The Probability Density Function  (PDF) of a continuous random variable gives the probability that any value in a continuous set of values might occur.

2) The probability that a random variable X takes a value in the interval [a,b] is given by integration of the probability function f(x).

$P( a\leq X \leq b)= \int\limits^a_b {f(x)} \ dx$ 

3) Now, Going towards the Question :D
 
If the random variable can take any real number , such that 
$a \to -\infty \;\:and \:\: b\to\infty$

$\int\limits^\infty_{-\infty} {f(x)} \, dx = 1$ 


Probabity is 1 ,as X will always be a real  number between $(-\infty,\infty)$ .