Discrete Random Variables (DRV)
Discrete Random Variables (DRV)
Given that \(X \sim \mathrm{B}(40, 0.64)\), find
- \(\mathrm{P}(X=28)\)
- \(\mathrm{P}(X > 21)\)
- \(\mathrm{P}(23.3 \le X \le 31.7)\)
- \(\mathrm{P}(X > 28.6)\)
- \(\mathrm{P}(|X - 31| < 4)\)
- \(\mathrm{P}(|X - 26| \ge 4)\)
- Probability that \(X\) lies within two standard deviations from the mean.
- Mode of \(X\).
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Answer:(i) \(0.0990\); (ii) \(0.910\); (iii) \(0.735\); (iv) \(0.170\); (v) \(0.268\); (vi) \(0.251\); (vii) probability \(0.954\), using mean \(25.6\) and variance \(9.216\); (viii) mode \(26\)
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