Question

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

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

Write the value of P (X ≤ 2).

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

$$\begin{gathered} \Rightarrow c+2c+4c+4c=1 \\ \Rightarrow 11c=1 \\ \Rightarrow c=\frac{1}{11} \\ \mathrm{Now}, \\ P\left(X\le 2\right)=P\left(X=1\right)+P\left(X=2\right)=\frac{1}{10}+\frac{2}{10}=\frac{3}{11} \end{gathered}$$