Statistics

Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3 , then new variance of the resulting observations is

If the sum of the deviations of 50 observations from 30 is 50 , then the mean of these observations is

Variance of first n natural numbers is $\_\_\_\_$.

The cumulative distribution function of a discrete random variable X is given by
$\mathrm{X}=x$-1012$\mathrm{F}(\mathrm{X}=\mathrm{x})$0.30.70.81
Then $E\left(\mathrm{X}^{2}\right)=$

A random variable X takes the values $0,1,2,3$ and its mean is 1.3 . If $\mathrm{P}(\mathrm{X}=3)=2 \mathrm{P}(\mathrm{X}=1)$ and $P(X=2)=0.3$, then $P(X=0)$ is

In an experiment with 15 observations for $x$, the following results were available $\sum x^{2}=2830, \sum x=170$. One observation 20 was found to be wrong and was replaced by the correct value 30 . Then the corrected variance is

Let $X\sim B(n,p)$, if $E(X)=5,Var(X)=2.5$, then $p(X<1)$ is equal to

If for some $x \in \mathbb{R}^{+} \cup\{0\}$, the frequency distribution of the marks obtained by 20 students in a test is
Marks :2357Frequency :(x+1)^{2}$$2 x-5$$x^{2}-3 x$$x
then the mean of the marks is

A random variable X assumes values $1,2,3, \ldots \ldots, \mathrm{n}$ with equal probabilities. If $\operatorname{var}(X): E(X)=4: 1$, then $n$ is equal to

The mean and variance of 7 observations are 8 and 16 respectively. If first five observations are 2, 4, 10, 12, 14, then absolute difference of remaining two observations is

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is 6.8 . Then which of the following gives possible values of $a$ and $b$ ?

The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14, then the product of remaining two observations is

Let mean and standard deviation of probability distribution
be $\mu$ and $\sigma$ respectively and if $\sigma-\mu=2$ then $\sigma=$