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STD 12 - 13. probability — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 13. probability1 Mark
MCQ
A random variable $X$ has Poisson’s distribution with mean $2$. Then $P(X > 1.5)$ equals
  • ✓
    $1 - \frac{3}{{{e^2}}}$
  • B
    $\frac{3}{{{e^2}}}$
  • C
    $\frac{2}{{{e^2}}}$
  • D
    $0$
✓

Answer

Correct option: A.
$1 - \frac{3}{{{e^2}}}$
a
(a) $P(x > 1.5) = 1 - P(x = 0) - P(x = 1)$
$P(x = k) = {e^{ - \lambda }}\frac{{{\lambda ^k}}}{{k!}}$
$\therefore$ $P(x > 1.5) = 1 - \frac{1}{{{e^2}}} - \frac{2}{{{e^2}}} = $ $1 - \frac{3}{{{e^2}}}$.

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