JEE Mains · Maths · STD 12 - 13. probability
There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable \(X\) denote the number of rotten apples. If \(\mu\) and \(\sigma^2\) represent mean and variance of \(X\), respectively, then \(10\left(\mu^2+\sigma^2\right)\) is equal to
- A \(20\)
- B \(250\)
- C \(25\)
- D \(30\)
Answer & Solution
Correct Answer
(A) \(20\)
Step-by-step Solution
Detailed explanation
\(\sum xP ( x )=\frac{6}{2}=\mu\) \(\sigma^2=\sum x^2 P(x)-\mu^2\) \(\sigma^2+\mu^2=0+\frac{1}{2}+\frac{12}{10}+\frac{9}{30}=2\) \(10\left(\sigma^2+\mu^2\right)=20 \text { Ans. }\)
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