Question
Download Solution PDFThe mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P(X = 1) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Given mean = 4
Variance = 2
∴ np = 4
and npq = 2
∴ 4q = 2, q = \(\frac{2}{4}\) = \(\frac{1}{2}\)
p = 1 - q = 1 - \(\frac{1}{2}\) = \(\frac{1}{2}\)
∴ n(\(\frac{1}{2}\)) = 4; n = 8
Thus
P(X = 1) = \({^8C_1 (\frac{1}{2}) (\frac{1}{2})^7}\)
= 8(\(\frac{1}{2}\))8 = \(\frac{8}{256}\) = \(\frac{1}{32}\)
Hence option 2 is correct
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