Question

If the random variable $X$ takes the values $ {{x}_{1}},{{x}_{2}},{{x}_{3}},....,{{x}_{10}} $ with probabilities $ p(X={{x}_{i}})=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} $
• E. $ \frac{3}{4} $

Answer 1

Answer: (C)

As we know, the sum of probability density function is one.
$ \therefore $ $ p(X={{x}_{1}})+p(X={{x}_{2}})+...+p(X={{x}_{10}})=1 $
$ \Rightarrow $ $ 1k+2k+3k+....+10k=1 $
$ \Rightarrow $ $ \frac{10(10+1)}{2}k=1 $
$ \Rightarrow $ $ k=\frac{1}{55} $