A random variable X has the following probability distribution: X… - Vidyadip

Question

A random variable X has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	K	2K	2K	3K	K²	2K²	7K²+ K

Determine:

K.
P(X < 3).
P(X > 6).
P(0 < X < 3).

✓

Answer

Here k + 2k + 2k + 3k + k² + 2k² + 7k² + k =1 $\Rightarrow$ 10k² + 9k –1 = 0
$\Rightarrow$ (10k – 1) (k + 1) = 0 $\Rightarrow$ k = $\frac{1}{10}$
$\therefore\text{ (i) k =}\frac{1}{10}$
(ii) P(x < 3) = 0 + k + 2k = 3k = $\frac{3}{10}$
(iii) P(x > 6) = 7k² + k = $\frac{7}{100}+\frac{1}{10}=\frac{17}{100}$
(iv) P(0 < x < 3) = k + 2k = 3k = $\frac{3}{10}$

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