Question
Download Solution PDFIf random variable X is binomially distributed with parameters n = 5, p = 0.4, the third factorial moment of Y equals
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula
The probability distribution function o Binomial distribution is give asfollows
F(x) = ncxpxqn – x
The factorial moment = ncrpr!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
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