The probability distribution of X is:

x 0 1 2 3 4
P(X = x) 0.1 2k k k 2k


Then var(X) =

1
\(\frac{3}{20}\)
2
\(\frac{9}{4}\)
3
\(\frac{141}{20}\)
4
\(\frac{159}{80}\)

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