Answer :

The probability distribution of X is:



We Know that



Therefore


k+3k+3k+k=1


8k=1





(1×k)+(2×3k)+(3×3k)+(4×k)


k+6k+9k+4k=20k




(12 ×k)+(22 ×3k)+(32 ×3k)+(42 ×k)


k+12k+27k+16k=56k



Var(X)=E(X2) - (E(X))2





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