Random Variables and its Probability Distributions

$d_i$ is the deviation of class mark $y_i$ from $"a"$ the assumed mean and $f_i$ is the frequency, if $M_g=x+\frac{1}{\sum f_i}\left(\sum f_i{d}_i\right)$, then $x$ is

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively, is

Let $X$ be a random variable taking values $x_1,x_2,\dots x_n$ with probabilities $p_1,p_2,\dots .,p_n$ respectively, then var $\left(x\right)$ is

Given $E\left(X+c\right)=8$ and $E\left(X-c\right)=12$. Then the value of $c$ is

A one-rupee coin, a two-rupee coin, a five coin and a ten-rupee coin are tossed simultaneously. Then the expected value of the sum of the values of coins that show heads up is

The p.d.f. of a continuous random variable $\mathrm{X}$ is given by $f\left(x\right)=\left\{\begin{array}{ll}\frac{x}{2},& 0<x<2\\ 0,& \text{ elsewhere }\end{array}\right.$. Then its mean is 

If the variance of a random variable $\mathrm{X}$ is $8$ and its mean is $2$ then the expectation of $X^2$ is 

If the probability mass function of $\mathrm{X}$ is given by the following table 

A die is tossed $50$ times and $\mathrm{\mu },\nu$ denotes the expected value of mean and variance respectively of number of times the face $4$ appears, then

If the probability distribution function of a random variable is given as
 

In a city $10$ accidents take place in a span of $50$ days. Assuming that the number of accidents follows the Poisson distribution, the probability that three or more accidents occur in a day, is

The variance of the first $50$ even natural numbers is

A random variable $X$ has the probability distribution given below.

Its variance is

For a random variable $X,E\left(X\right)=3$ and $E\left(X^2\right)=11.$ Then, variance of $X$ is

If the random variable $X$ takes the values $x_1, x_2, ........., x_{10}$ with probability $P\left(X=x_i\right)=ki,$ then the value of $k$ is equal to

A random variable $X$ can attain only the value$1, 2, 3, 4, 5$ with respective probabilities $k, 2k, 3k, 2k, k$. If $m$ is the mean of the probability distribution, then $\left(k,m\right)$ is equal to

A manufacturer of copper pins knows that $5\%$of his product are defective. He sells pins in boxes of $100$and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is

At a telephone enquiry system the number of phone calls regarding relevant enquiry follow poisson distribution with an average of $5$ phone calls during $10$ min time intervals. The probability that there is at the most one phone cell during a $10$min time period, is

The probability distribution of a random variable $X$ is given as 

A random variable $X$ has Poisson distribution with mean $2$. The $P\left(X>1.5\right)$ equals