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Discrete Random Variables (DRV) - Mode of a Binomial Distribution

Discrete Random Variables (DRV) - Mode of a Binomial Distribution

Given that \(X\sim\mathrm{B}(25,0.35)\), find

  1. \(\mathrm{P}(X=10)\)
  2. \(\mathrm{P}(X>12)\)
  3. \(\mathrm{P}(8.12 < X\le 14.36)\)
  4. \(\mathrm{P}(X\ge 17.3)\)
  5. \(\mathrm{P}\left( \left| X-10 \right|<9 \right)\)
  6. \(\mathrm{P}(\left| X-12 \right|>3)\)
  7. Probability that \(X\) lies within one standard deviation from the mean.
  8. Mode of \(X\).

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Answer:(i) \(0.141\); (ii) \(0.0604\); (iii) \(0.524\); (iv) \(0.000181\); (v) \(0.99966\); (vi) \(0.470\); (vii) \(0.701\); (viii) Mode = \(9\)

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