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

$$\begin{gathered} \Rightarrow k+2k+3k+4k=1 \\ \Rightarrow 10k=1 \\ \Rightarrow k=\frac{1}{10} \\ \mathrm{Now}, \\ P\left(X\ge 3\right)=P\left(X=3\right)+P\left(X=4\right)=\frac{3}{10}+\frac{4}{10}=\frac{7}{10} \end{gathered}$$