Question

The probability distribution of a random variable X is given below:

x	0	1	2	3
P(X)	k	$$\frac{k}{2}$$	$$\frac{k}{4}$$	$$\frac{k}{8}$$

Determine the value of k .

Answer 1

We have,
The probability distribution of a random variable X is given below:

x	0	1	2	3
P(X)	k	$$\frac{k}{2}$$	$$\frac{k}{4}$$	$$\frac{k}{8}$$

$$\text{ As },\sum p_i=1$$
$$\Rightarrow k+\frac{k}{2}+\frac{k}{4}+\frac{k}{8}=1$$
$$\Rightarrow \frac{8k+4k+2k+k}{8}=1$$
$$\Rightarrow \frac{15k}{8}=1$$
$$\therefore k=\frac{8}{15}$$