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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

Let X and Y be two random variables such that X+Y=100 . If X...

Let XX and YY be two random variables such that X+Y=100\mathrm{X}+\mathrm{Y}=100. If X follows Binomial distribution with parameters n=100n=100 and p=46p=\frac{4}{6}, what is the variance of YY ?

Options

  1. A11
  2. B12\frac{1}{2}
  3. C1616
  4. D116\frac{1}{16}

Correct answer

C. 1616

Step-by-step solution

var⁡(X)=npq=100×45×15=16var⁡(Y)=var⁡(100−X)=var⁡(X)=16\operatorname{var}(X)=n p q=100 \times \frac{4}{5} \times \frac{1}{5}=16\operatorname{var}(Y)=\operatorname{var}(100-X)=\operatorname{var}(X)=16
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