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Question

(A) The total number of ways to select $2$ numbers from $6$ is $\binom{6}{2} = \frac{6 	imes 5}{2} = 15$. Let $X$ be the larger of the two numbers. T

Vedclass · Accepted Answer

$\frac{14}{3}$

Vedclass · Answer

(A) The total number of ways to select $2$ numbers from $6$ is $\binom{6}{2} = \frac{6 	imes 5}{2} = 15$. Let $X$ be the larger of the two numbers. The possible values for $X$ are $2, 3, 4, 5, 6$. If $X = 2$,the pair is $(1, 2)$,so $P(X=2) = \frac{1}{15}$. If $X = 3$,the pairs are $(1, 3), (2, 3)$,so $P(X=3) = \frac{2}{15}$. If $X = 4$,the pairs are $(1, 4), (2, 4), (3, 4)$,so $P(X=4) = \frac{3}{15}$. If $X = 5$,the pairs are $(1, 5), (2, 5), (3, 5), (4, 5)$,so $P(X=5) = \frac{4}{15}$. If $X = 6$,the pairs are $(1, 6), (2, 6), (3, 6), (4, 6), (5, 6)$,so $P(X=6) = \frac{5}{15}$. The expected value $E(X) = \sum x P(X=x) = 2(\frac{1}{15}) + 3(\frac{2}{15}) + 4(\frac{3}{15}) + 5(\frac{4}{15}) + 6(\frac{5}{15})$. $E(X) = \frac{2 + 6 + 12 + 20 + 30}{15} = \frac{70}{15} = \frac{14}{3}$.

$X=x$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

$X=x$	$1$	$2$	$3$
$P(X=x)$	$1/5$	$2/5$	$2/5$

Two numbers are selected at random,without replacement from the first $6$ positive integers. Let $X$ denote the larger of the two numbers. Then $E(X) = $

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