A discrete random variable X has the probability distribution giv… - Vidyadip

Question

A discrete random variable X has the probability distribution given below:

X:	0.5	1	1.5	2
P(X):	k	k²	2k²	k

Find the value of k.

✓

Answer

We know that,
P(0.5) + P(1) + P(1.5) + P(2) = 1
k + k²+ 2k² + k = 1
3k² + 2k - 1 = 0
3k² + 3k - k - 1 = 0
(3k - 1)(k + 1) = 0
$\text{k}=\frac{1}{3}$ or $\text{k}=-1$
We know that $0\leq\text{P}(\text{X})\leq1$
$\therefore\ \text{k}=\frac{1}{3}$

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