Mathematical Expectation

A coin is biased so that the head is $3$ times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin, then the mean of $X$ is

Find the mean number of heads in three tosses of a fair coin:

In a random experiment of throwing $5$ coins, the number of heads is defined as a random variable. The mean of the random variable is

$d_i$ 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

In a normal distribution, $31\%$ of the items are under $45$ and $8\%$ are over $64$. Determine the mean and variance of the distribution.

In a normal distribution, $7\%$ of the items are under $35$ and $89\%$ are under $63$. Determine the variance of the distribution.

Let a pair of dice be thrown and the random variable $X$ be the absolute value of the difference of the numbers that appear on the two dice. The expectation value $E\left(X\right)$ of $X$ is

Suppose $X$ is normal with mean $10$. If $P(X>16)=0.0228$, then what is the variance of $X$? [Use $\Phi \left(2\right)=0.9772$]

Suppose $X$ is normal with mean $8$. If $P(X>16)=0.0228$, then what is the variance of $X$? [Use $\Phi \left(2\right)=0.9772$]

Suppose $X$ is normal with mean $4$. If $P(X>16)=0.0228$, then what is the variance of $X$? [Use $\Phi \left(2\right)=0.9772$]

Suppose $X$ is normal with mean $2$. If $P(X>16)=0.0228$, then what is the variance of $X$? [Use $\Phi \left(2\right)=0.9772$]

Suppose $X$ is normal with mean $6$. If $P(X>16)=0.0228$, then what is the variance of $X$? [Use $\Phi \left(2\right)=0.9772$]

State the properties of mean or expectation and variance. For the random variable $X$ with the given probability mass function as below, find the mean and variance.

$f\left(x\right)=\left\{\begin{array}{r}2(x-1)\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1<x<2\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} \mathrm{otherwise} \end{array}\right.$

State the properties of mean or expectation and variance. For the random variable $X$ with the given probability mass function as below, find the mean and variance.

$f\left(x\right)=\left\{\frac{4-x}{6}, x=1,2,3\right.$

State the properties of mean or expectation and variance. For the random variable $X$ with the given probability mass function as below, find the mean and variance.

$f\left(x\right)=\left\{\begin{array}{cc}\frac{1}{10}& x=2,5\\ \frac{1}{5}& x=0,1,3,4\end{array}\right.$

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

Two numbers are selected at random (without replacement) from the first six positive integers. If $X$ denotes the smaller of the two numbers, then the expectation of $X$, is

A box contains $6$ red ball and $2$ black balls. Two balls are drawn at random from it without replacement. If $X$ denotes the number of red balls drawn, then $E\left(X\right)$ is equal to

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