The whole question is:   

Let X be a discrete random variable and let Y = 0.5 X + 3.  

(i) Assume that the PMF of X is given by  

![enter image description here](https://i.stack.imgur.com/q0aPb.png)  

where k is some suitable constant. Determine the value of k.

(ii) Find E [X] and Var[X].  

(iii) Given that X has the PMF found above, find the PMF of Y .  

(iv) Without explicit calculation from the PMF of Y , find E [Y ] and V ar[Y ].  

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I have to do this for homework but I'm getting E[X] = 0 and can't find variance either.

**My progress so far:**

`Pr(X = -4) + Pr(X = -2) + Pr(X = 0) + Pr(X = 2) + Pr(X = 4) = 1
k * -4^2 + k * -2^2 + k * 0^2 + k * 2^2 + k * 4^2 = 1
16k + 4k + 0 + 4k + 16k = 1
40k = 1
k = 1/40`

Distribution table:
`x | -4 | -2 | 0 | 2 | 4 |
Pr(X = x) | 0.4 | 0.1 | 0.0 | 0.1 | 0.4 |`

Then:
`E[X] = -4 * 0.4 + -2 * 0.1 + 0 * 0 + 2 * 0.1 + 4 * 0.4
 = -1.6 + -0.2 + 0 + 0.2 + 1.6
 = 0`

Is this the correct answer till now? If so, how should I proceed with Var[X]?

Any help will be greatly appreciated!