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How do you determine the probability distribution of P(x>5)?

The table: x ---- 4 ---- 5 ----- 6 ----- 7 ----- 8 P(x) ---0.1----0.1---0.2-----0.1----0.5

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Explanation

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Explanation:

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Steve M Share
Mar 6, 2017

$P \left(X > 5\right) = 0.8$

Explanation:

The standard notation is to use a lower case letter to represent an actual event, and an upper case letter for the Random Variable used to measure the probability of the event occurring.

Thus the correct table would be:

And then;

$P \left(X > 5\right) = P \left(X = 6 \mathmr{and} X = 7 \mathmr{and} X = 8\right)$
$\text{ } = P \left(X = 6\right) + P \left(X = 7\right) + P \left(X = 8\right)$
$\text{ } = 0.2 + 0.1 + 0.5$
$\text{ } = 0.8$

Alternatively:

$P \left(X > 5\right) = 1 - P \left(X \le 5\right)$
$\text{ } = 1 - P \left(X = 4 \mathmr{and} X = 5\right)$
$\text{ } = 1 - \left\{P \left(X = 4\right) + P \left(X = 5\right)\right\}$
$\text{ } = 1 - \left(0.1 + 0.1\right)$
$\text{ } = 0.8$, as before

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