AP EAMCET · Maths · Probability
If a random variable X satisfies poisson distribution with a mean value of 5 , then probability that \(\mathrm{X} \lt 3\) is
- A \(\frac{37}{2} e^5\)
- B \(6 e^5\)
- C \(6 e^{-5}\)
- D \(\frac{37}{2} e^{-5}\)
Answer & Solution
Correct Answer
(D) \(\frac{37}{2} e^{-5}\)
Step-by-step Solution
Detailed explanation
Given \(x\) satisfies poisson with mean value is 5 So, \(\mathrm{P}(x \lt 3)=\mathrm{P}(x=0)+\mathrm{P}(x=1)+\mathrm{P}(x=2)\) \(=e^{-5} \frac{5^0}{0!}+e^{-5} \frac{5^1}{1!}+e^{-5} \frac{5^2}{2!}\) \(=e^{-5}\left(1+5+\frac{25}{2}\right)=\frac{37}{2} e^{-5}\)
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