# Thread: Discrete Random Variable Question [S1]

1. ## Discrete Random Variable Question [S1]

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?

2. Originally Posted by db5vry
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.
P(X = 3) $\displaystyle \geq 0$

P(X = 2) $\displaystyle \leq 1$

3. Originally Posted by Isomorphism
P(X = 3) $\displaystyle \geq 0$

P(X = 2) $\displaystyle \leq 1$
For the standard deviation of X, I had 0.75 to 2 decimal places and for E (1/X) I had a value of 17.5.

Are these values correct?

Thank you for your help :]