Statistics · Mathematics · MHT CET

If both mean and variance of 50 observations $$x_1, x_2, \ldots, x_{50}$$ are equal to 16 and 256 respectively, then mean of $$\left(x_1-5\right)^2,\l...

The p.m.f. of a random variable $$\mathrm{X}$$ is $$\mathrm{P}(x)=\left\{\begin{array}{cl}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \mat...

The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

Variance of first $$2 n$$ natural numbers is

If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then the value of $$p$$ is

The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$ $$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0...

If a continuous random variable $$\mathrm{X}$$ has probability density function $$\mathrm{f}(x)$$ given by $$f(x)=\left\{\begin{array}{cl} a x & , \te...

The raw data $$x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$$ is an A.P. with common difference $$\mathrm{d}$$ and first term $$0, \bar{x}$$ and $$\sigma^2...

The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a probability $$\frac{1}{\mathrm{...

For 20 observations of variable $x$, if $$\sum\left(x_i-2\right)=20$$ and $$\sum\left(x_i-2\right)^2=100$$, then the standard deviation of variable $$...

If the variance of the numbers $$-1,0,1, \mathrm{k}$$ is 5, where $$\mathrm{k} > 0$$, then $$\mathrm{k}$$ is equal to

If both mean and variance of 50 observations $$x_1, x_2, \ldots \ldots, x_{50}$$ are equal to 16 and 256 respectively, then mean of $$\left(x_1-5\righ...

If variance of $$x_1, x_2 \ldots \ldots, x_n$$ is $$\sigma_x^2$$, then the variance of $$\lambda x_1, \lambda x_2, \ldots \ldots, \lambda x_{\mathrm{n...

Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, then new variance of the resulting observatio...

The variance, for first six prime numbers greater than 5, is

If the mean and S.D. of the data $$3,5,7, a, b$$ are 5 and 2 respectively, then $$a$$ and $$b$$ are the roots of the equation

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

The standard deviation of the following distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;b...

The variance and mean of 15 observations are respectively 6 and 10 . If each observation is increased by 8 then the new variance and new mean of resul...

Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students in a class. Then subject show...

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are

For X ~ B(n, p), if p = 0.6, E(X) = 6, then Var(X) =

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3 , ₹ 1.5 and ₹ 1. The demands for these cakes are...

For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance...

If the variance of the numbers $$2,3,11$$ and $$x$$ is $$\frac{49}{4}$$, then the values of $$x$$ are

If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is

If the p.m.f of a. r.v. $$X$$ is given by $$P(X=x)=\frac{{ }^5 C_x}{2^5}$$ if $$x=0,1,2, \ldots \ldots . .5=0$$, 0 , otherwise, then which of the foll...