For a given probability distribution f(x) = (1/8) C(3, x), x = 0, 1, 2, 3किसी दिए गए संभाव्यता वितरण
For a given probability distribution
f(x) = (1/8) C(3, x), x = 0, 1, 2, 3
for a random variable X, the moment generating function of this is
किसी दिए गए संभाव्यता वितरण
f(x) = (1/8) C(3, x), x = 0, 1, 2, 3
के लिए यादृच्छिक चर X का आघूर्ण-जनक फलन है
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Correct answer: (C) (1/8)(1 + eᵗ)³(1/8)(1 + eᵗ)³
Explanation
M(t) = Σ eᵗˣ (1/8) C(3, x) = (1/8) Σ C(3, x)(eᵗ)ˣ = (1/8)(1 + eᵗ)³ by the binomial theorem.M(t) = Σ eᵗˣ (1/8) C(3, x) = (1/8) Σ C(3, x)(eᵗ)ˣ = (1/8)(1 + eᵗ)³ (द्विपद प्रमेय से)।