JEE Mains · Maths · STD 12 - 13. probability
Let \(X\) be a random variable having binomial distribution \(B (7, p )\). If \(P ( X =3)=5 P ( X =4)\), then the sum of the mean and the variance of \(X\) is
- A \(\frac{105}{16}\)
- B \(\frac{77}{36}\)
- C \(\frac{7}{16}\)
- D \(\frac{49}{16}\)
Answer & Solution
Correct Answer
(B) \(\frac{77}{36}\)
Step-by-step Solution
Detailed explanation
\(B (7, p)\) \(n =7 \quad p = p\) given \(P(x=3)=5 P(x=4)\) \({ }^{7} C_{3} \times p^{3}(1-p)^{4}=5^{7} C_{4} p^{4}(1-p)^{3}\) \(\frac{{ }^{7} C_{3}}{5 \times{ }^{7} C_{4}}=\frac{p}{1-p}\) \(1- p =5 p\) \(6 p =1\) \(p=\frac{1}{6} \Rightarrow q=\frac{5}{6}\) \(n =7\) Mean…
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