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