Question

If the probability distribution of a random variable X is as given below:

Write the value of P (X ≤ 2).

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

 

 

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

\[\Rightarrow c + 2c + 4c + 4c = 1\]
\[ \Rightarrow 11c = 1\]
\[ \Rightarrow c = \frac{1}{11}\]
\[\text{ Now } , \]
\[P\left( X \leq 2 \right) = P\left( X = 1 \right) + P\left( X = 2 \right) = \frac{1}{10} + \frac{2}{10} = \frac{3}{11}\]