The discrete random variable X has the following probability distribution.

x = 1, 2. 3 for respective values of

P(X = x) = θ, 2θ, (1 – 3θ)

(a) State the range of possible values of the constant θ. [2]

(b) Given that E(X) = 2·2,

(i) show that θ = 0·2,

(ii) calculate the standard deviation of X,

(iii) evaluate E(1/X) . [10]

I should be able to do the final parts of this question, but how do I do part a]? I am at a loss for how to approach it despite it looking fairly simple. Could someone please help?