statistic

there's something missing

Consider that y=f(k,x) & you've given x=1,2,...5 what are the corresponding y's\

IOW We need y1,y2,...y5 to predict k

Rap

The values of f(x) must be non-negative and sum to 1. Therefore:
(k+4k+9k+16k+25k)/30=1
You should be able to figure out part (a) from that.

Given that P(x) = f(x) is the probability of x being selected, and now knowing the value of k, it should be easy to figure out P(2)+P(4) and P(3)+P(4)+P(5).