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(A) Let $H$ be the number of heads and $T$ be the number of tails in $6$ tosses. Since the total number of tosses is $6$,we have $H + T = 6$,which imp

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$0, 2, 4, 6$

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(A) Let $H$ be the number of heads and $T$ be the number of tails in $6$ tosses. Since the total number of tosses is $6$,we have $H + T = 6$,which implies $T = 6 - H$.The random variable $X$ is defined as the absolute difference between the number of heads and tails: $X = |H - T|$.Substituting $T = 6 - H$,we get $X = |H - (6 - H)| = |2H - 6|$.Since $H$ can take values from $0$ to $6$,we calculate $X$ for each case:If $H = 0, T = 6$,then $X = |0 - 6| = 6$.If $H = 1, T = 5$,then $X = |1 - 5| = 4$.If $H = 2, T = 4$,then $X = |2 - 4| = 2$.If $H = 3, T = 3$,then $X = |3 - 3| = 0$.If $H = 4, T = 2$,then $X = |4 - 2| = 2$.If $H = 5, T = 1$,then $X = |5 - 1| = 4$.If $H = 6, T = 0$,then $X = |6 - 0| = 6$.Thus,the set of possible values for $X$ is $\{0, 2, 4, 6\}$.

$X = x_{i}$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x_{i})$	$0.1$	$k$	$0.2$	$2k$	$3k$	$k$

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/10$	$2/10$	$3/10$	$4/10$

$Z$	$3$	$2$	$1$	$0$	$-1$
$P(Z)$	$0.3$	$0.2$	$0.4$	$0.1$	$0.05$

Let $X$ represent the difference between the number of heads and the number of tails obtained when a coin is tossed $6$ times. What are the possible values of $X$?

Similar Questions

$A$ random variable $X$ has the following distribution.
$X = x_{i}$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x_{i})$ $0.1$ $k$ $0.2$ $2k$ $3k$ $k$

Then the variance of this distribution is

The probability distribution of a random variable $X$ is given by:
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/10$ $2/10$ $3/10$ $4/10$

Then the cumulative distribution function (c.d.f.) $F(x)$ of $X$ is given by:

If the probability distribution of a random variable $X$ is as follows,then the mean of $X$ is:
$X = x_i$ $-1$ $0$ $1$ $2$
$P(X = x_i)$ $k^3$ $2k^3 + k$ $4k - 10k^2$ $4k - 1$

State which of the following is not the probability distribution of a random variable. Give reasons for your answer.

$Z$ $3$ $2$ $1$ $0$ $-1$

$P(Z)$ $0.3$ $0.2$ $0.4$ $0.1$ $0.05$

$A$ coin is tossed until one head appears or a tail appears $4$ times in succession. The probability distribution of the number of tosses $X$ is:

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