Question

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

X	0.5	1	1.5	2
P(X)	k	k2	2k2	k

Find the value of k

Answer 1

For a probability distribution, we know that if P_i ≥ 0

`sum_("i" = 1)^"n" "P"_"i"` = 1

⇒ k + k² + 2k² + k = 1

⇒ 3k2 + 2k – 1 = 0

⇒ 3k² + 3k – k – 1 = 0

⇒ 3k(k + 1) – 1(k + 1) = 0

⇒ (3k – 1)(k + 1) = 0

∴ k = `1/3` and k = – 1

But k ≥ 0

∴ k = `1/3`