Consider a game of tossing a six-sided fair d | vedclass

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(A) Let $X$ be the random variable representing the winning amount. The probability of each face $k$ appearing is $P(k) = 1/6$ for $k \in \{1, 2, 3, 4

Vedclass · Accepted Answer

$77$/$10$

Vedclass · Answer

(A) Let $X$ be the random variable representing the winning amount. The probability of each face $k$ appearing is $P(k) = 1/6$ for $k \in \{1, 2, 3, 4, 5, 6\}$.The winning amount for a face $k$ is $W(k) = \frac{36}{k} - 2k$.The expected value $E[X]$ is given by $\sum_{k=1}^{6} W(k) \cdot P(k)$.$E[X] = \frac{1}{6} \sum_{k=1}^{6} \left(\frac{36}{k} - 2k\right) = \frac{1}{6} \left[\left(\frac{36}{1} - 2\right) + \left(\frac{36}{2} - 4\right) + \left(\frac{36}{3} - 6\right) + \left(\frac{36}{4} - 8\right) + \left(\frac{36}{5} - 10\right) + \left(\frac{36}{6} - 12\right)\right]$.$E[X] = \frac{1}{6} \left[34 + 14 + 6 + 1 - \frac{14}{5} - 6\right]$.$E[X] = \frac{1}{6} \left[49 - \frac{14}{5}\right] = \frac{1}{6} \left[\frac{231}{5}\right] = \frac{77}{10}$.

$X = x_i$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
$P(X = x_i)$	$10k$	$9k$	$8k$	$8k$	$6k$	$5k$	$4k$	$3k$	$k$

$X=x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X=x)$	$0$	$K$	$2K$	$2K$	$3K$	$K^2$	$2K^2$	$7K^2+K$

Consider a game of tossing a six-sided fair die. If the face that comes up is $k$, the player wins Rs. $36/k$ and loses Rs. $2k$, where $k \in \{1, 2, 3, 4, 5, 6\}$. What is the expected winning amount in this game in Rs.?

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$X=x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
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Then,$P(0 < X < 5)$ is equal to:

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