The random variable X can take only the values 0, 1, 2, 3. Given that and such that find the value of p.

Question

The random variable X can take only the values 0, 1, 2, 3. Given that   and  such that  find the value of p.

Philoid · Accepted Answer

Given; Random variable X can take only the values 0, 1, 2,

3.

P(X=0) = P(X=1) = p and P(X=2) = P(X=3) = q and

⇒ P(X=0) + P(X=1) + P(X=2) + P(X=3) = 1

∴ 2p + 2q = 1 ……(i)

∴ 0 + p + 4q + 9q = 2(0 + p + 2q + 3q)

∴ p − 3q = 0 ……(ii)

From (i) and (ii)