A random variable X has the following di

CUET Preparation Today

Start Free Mocks

Home Questions ST9DUMVFYM

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Probability

Question:

A random variable X has the following distribution :

X	0	1	2	3	4	5	6	7
P(X)	0	$3k$	$k$	$2k$	$3k^2$	$k^2$	$6k^2$	$3k$

The value of k is :

Options:

$\frac{1}{10}$

-1

$\frac{-1}{10}$

$\frac{1}{9}$

Correct Answer:

$\frac{1}{10}$

Explanation:

The correct answer is Option (1) → $\frac{1}{10}$

$∑P_i(x_i)=1$

$9k+10k^2=1$

$10k^2+9k-1=0$

$10k^2+10k-k-1=0$

$10k(k+1)-1(k+1)=0$

$(10k-1)(k+1)=0$

so $k=\frac{1}{10}$ as $k≠-1$