Test by Bikram | Mock GATE | Test 2 | Question: 50

Question

A random variable has the Probability Density Function (PDF)
 $f(x) = \begin{cases}3x^2&; 0 < x < 1\\  0&; otherwise \end{cases}$

Then $P\left ( x\leqslant 1/2 \right )=$ __________

Answer 1

Sum of all probability = 1
Equation given in box is true for every Probability Density Function f(x).
 

Comments

Why not 0.25??? 1/(1/2-0) =2=k.

Now integrating it kf(x)dx from 0 t0 1/2 should give 0.25

---

Sir, I am unable to understand why are you finding k ? Whats the use of it ?

We are given PDF , We want Cumulative Probability Distribution function, we can just integrate from

-inf upto 0.5.

---

Can we say that ‘k’ is the rate at which probability is changing? Sort of finding out what kind of a distribution this probability would follow?