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Probability — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsProbability1 Mark
MCQ
If a random variable X has the Poisson distribution with mean 2. Then, $P(X > 1.5)$ is:
  • A
    $2 e^{-2}$
  • B
    $3 e^{-2}$
  • C
    $1-2 e^{-2}$
  • ✓
    $1-3 e^{-2}$
✓

Answer

Correct option: D.
$1-3 e^{-2}$
(D) $1-3 e^{-2}$
Explanation: We know that,
$P(X=x)=\frac{e^{-\lambda} \lambda^x}{x!}$
Given that mean $=2=\lambda$
$\therefore \quad P(X>1.5)=P(X=2)+P(X=3)+\ldots$
$\Rightarrow  P(X>1.5)=1-[P(X=0)+P(X=1)]$
$=1-\left|e^{-2}+2 e^{-2}\right|=1-3 e^{-2}$

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