JEE Mains · Maths · STD 12 - 13. probability
A random variable X takes values 0, 1, 2, 3 with probabilities \( \frac{2a+1}{30},\frac{8a-1}{30},\frac{4a+1}{30} \), b respectively, where \( a, b\in R \). Let μ and σ respectively be the mean and standard deviation of X such that \( \sigma^{2}+\mu^{2}=2 \). Then \( \frac{a}{b} \) is equal to :
- A 30
- B 3
- C 60
- D 12
Answer & Solution
Correct Answer
(C) 60
Step-by-step Solution
Detailed explanation
x 0 1 2 3 p( x ) \(\frac{2 a+1}{30}\) \(\frac{8 a-1}{30}\) \(\frac{4 a+1}{30}\) b \( \sigma^{2}=\sum x_{i}^{2}p(x_{i})-\mu^{2} \) \( \sigma^{2}+\mu^{2}=\sum x_{i}^{2}p(x_{i}) \) \( =0+1(\frac{8a-1}{30})+4(\frac{4a+1}{30})+9b \) \( \Rightarrow\frac{24a+270b+3}{30}=2 \)…
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