From a lot of $12$ items containing $3$ defectives, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $n-m$ is equal to..........
From a lot of $12$ items containing $3$ defectives, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $n-m$ is equal to..........
- [JEE MAIN 2024]
- A
$71$
- B
$34$
- C
$72$
- D
$76$
Similar Questions
The data is obtained in tabular form as follows.
${x_i}$
$60$
$61$
$62$
$63$
$64$
$65$
$66$
$67$
$68$
${f_i}$
$2$
$1$
$12$
$29$
$25$
$12$
$10$
$4$
$5$
The data is obtained in tabular form as follows.
| ${x_i}$ | $60$ | $61$ | $62$ | $63$ | $64$ | $65$ | $66$ | $67$ | $68$ |
| ${f_i}$ | $2$ | $1$ | $12$ | $29$ | $25$ | $12$ | $10$ | $4$ | $5$ |
Find the variance of the following data: $6,8,10,12,14,16,18,20,22,24$
Find the variance of the following data: $6,8,10,12,14,16,18,20,22,24$
For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is
For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is
- [AIEEE 2010]
If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to
If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to
- [JEE MAIN 2019]
The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject
Mathematics
Physics
Chemistty
Mean
$42$
$32$
$40.9$
Standard deviation
$12$
$15$
$20$
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
| Subject | Mathematics | Physics | Chemistty |
| Mean | $42$ | $32$ | $40.9$ |
| Standard deviation | $12$ | $15$ | $20$ |
Which of the three subjects shows the highest variability in marks and which shows the lowest?