Q. If the random variable $X$ takes the values $x_{1},\ x_{2},x_{10}$ with probability $P\left( X = x_{1} \right) = ki,$ then the value of $k$ is equal to
A) $\frac{1}{10}$
B) $\frac{1}{4}$
C) $\frac{1}{55}$
D) $\frac{7}{12}$
Explanation
(c)
As we know, the sum of probability density function is one.
$\therefore P\left( X = x_{1} \right) + P\left( X = x_{2} \right) + ... + P\left( X = x_{10} \right) = 1$
$\Rightarrow \ 1k + 2k + 3k + ... + 10k = 1$
$\Rightarrow \ \frac{10(10 + 1)}{2}k = 1$
$\Rightarrow \ k = \frac{1}{55}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.