Question

A random variable has the following probability distribution: 

X = xi :	1	2	3	4
P (X = xi) :	k	2k	3k	4k

Write the value of P (X ≥ 3).

 

Answer 1

We know that the sum of probabilities in a probability distribution is always 1.

∴ P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1

\[\Rightarrow k + 2k + 3k + 4k = 1\]
\[ \Rightarrow 10k = 1\]
\[ \Rightarrow k = \frac{1}{10}\]
\[\text{ Now} , \]
\[P\left( X \geq 3 \right) = P\left( X = 3 \right) + P\left( X = 4 \right) = \frac{3}{10} + \frac{4}{10} = \frac{7}{10}\]