Question
Download Solution PDFIf mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Binomial distribution The binomial distribution formula is:P (X = r) =
P(X) = probability of a success on an individual trial
p = probability of “success”
r = number of success
q = probability of “failure” OR q = 1- p
n = number of trials
- Mean = np
- Variance = npq
Calculation:
Given: mean = 2, variance = 1
We know p + q = 1
So, p = 1 - ½ = ½
mean = 2
⇒ np = 2
⇒ n = 2/p
= 4
We know P(required) = 1 – P (not required)
P (X > 1) = 1 – P (X = 0) – P (X = 1)
Hence, option (4) is correct
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