A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P (X =3) = 2P (X = 1) and P(X = 2) = 0.3, then P(X = 0) is

Question

Philoid · Accepted Answer

Let the value P(X=0) be x and the value of P(X=1) be A

GIVEN- P(X=3) =2P(X=1)

=2(A) =2A

P(X=2) =0.3

So, The Probability distribution of X is

Mean of E(X) =1.3

⇒ (0×x)+(1×A)+(2×0.3)+(3×2A)=1.3

⇒ A+0.6+6A=1.3

⇒ 7A+0.6=1.3

⇒ 7A=0.7

⇒ A=0.1

By putting the value of A in probability distribution, we get

We Know that

Therefore,

⇒ x+0.1+0.3+0.2=1

x=1-0.6

x=0.4