Question

If random variable X is binomially distributed with parameters n = 5, p = 0.4, the third factorial moment of Y equals
1. 0.384
2. 3.84
3. 0.768
4. 7.68

Answer 1

Correct Answer - Option 2 : 3.84

Formula

The probability distribution function o Binomial distribution is give asfollows

F(x) = ⁿc_xp^xq^{n – x}

The factorial moment = ⁿc_rp^r!r

X = 0, 1, 2 ---n

p = Probability of success event

q = 1 – p = Probability of failure of event.

Calculation

According to the formula of factorial moment of binomial distribution

⇒ E[(X)_r] =  ⁵c₃(0.4)³!3

⇒ [5!/(3!(5 – 3)!](0.4 × 0.4 × 0.4)!3

⇒ [5!/3! × 2!](0.064(3)

∴ The value of E[(X)_r] is 3.84