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

X 2 3 4 5 P(x) $\Large\frac{5}{k}$ $\Large\frac{7}{k}$ $\Large\frac{9}{k}$ $\Large\frac{11}{k}$ The value of k is $(A)\;8\quad(B)\;16\quad(C)\;32\quad(D)\;48$

Toolbox:
• For a probability distribution.
• $\sum p_{i}=1$
• The total sum of probability should be equal to 1.
$\sum p_{i}=\large\frac{5}{R}+\frac{7}{R}+\frac{9}{R}+\frac{11}{R}=1$
=$\large\frac{32}{R}=1$
$\Rightarrow R=32$
$'C'$ option is correct.