NDA Mathematics 21 April 2024 | Statistics Question 2 | Mathematics

If two random variables $X$ and $Y$ are connected by relation $\frac{2 X-3 Y}{5 X+4 Y}=4$ and $X$ follows Binomial distribution with parameters $n=10$ and $p=\frac{1}{2}$, then what is the variance of $Y$ ?

$\frac{810}{361}$

$\frac{9}{19}$

$\frac{21}{361}$

$\frac{121}{361}$

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

An edible oil is sold at the rates 150, 200, 250, 300 rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family in every year during these years, what is the average price of oil in rupees (approximately) per litre?

210

220

230

240

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next two (02) items that follow:

$x_i$	1	2	3	...	$n$
$f_i$	1	$2^{-1}$	$2^{-2}$	...	$2^{-(n-1)}$

$$ \text { What is } \sum_i^n x_i f_i \text { equal to? } $$

$\frac{2^{n+1} - n + 2}{2^{n-1}}$

$\frac{2^{n+1} - n - 2}{2^{n-1}}$

$\frac{2^{n+1}+n+2}{2^{n-1}}$

$\frac{2^{n+1}-n-2}{2^n}$

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next two (02) items that follow:

$x_i$	1	2	3	...	$n$
$f_i$	1	$2^{-1}$	$2^{-2}$	...	$2^{-(n-1)}$

What is the mean of the distribution?

$\frac{2^{n+1} - n + 2}{2^{n}-1}$

$\frac{2^{n+1} - n - 2}{2^{n-1}}$

$\frac{2^{n+1} - n - 2}{2^{n}-1}$

$\frac{2^{n+1} - n + 2}{2^n}$

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