A person who tosses an unbiased coin gains tw | vedclass

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Question

(C) Let $H$ denote a head and $T$ denote a tail. For each $H$, the gain is $+2$ points, and for each $T$, the loss is $-1$ point.When three coins are

Vedclass · Accepted Answer

$\{-3, 0, 3, 6\}$

Vedclass · Answer

(C) Let $H$ denote a head and $T$ denote a tail. For each $H$, the gain is $+2$ points, and for each $T$, the loss is $-1$ point.When three coins are tossed, the possible outcomes for the number of heads $(n_H)$ and tails $(n_T)$ are as follows:$1$. Three tails $(0H, 3T)$: Score $X = 0(2) + 3(-1) = -3$.$2$. Two tails and one head $(1H, 2T)$: Score $X = 1(2) + 2(-1) = 2 - 2 = 0$.$3$. One tail and two heads $(2H, 1T)$: Score $X = 2(2) + 1(-1) = 4 - 1 = 3$.$4$. Three heads $(3H, 0T)$: Score $X = 3(2) + 0(-1) = 6$.Thus, the possible values for the total score $X$ are $\{-3, 0, 3, 6\}$.Therefore, the range of $X$ is $\{-3, 0, 3, 6\}$.

$X$	$1$	$2$	$3$	$4$	$5$
$P(X=x)$	$K$	$2K$	$3K$	$2K$	$K$

$X$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X)$	$0.1$	$0.2$	$0.2$	$0.3$	$0.15$	$0.05$

$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ is

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