Question

the random variable x has the following discrete probability distribution
x 10 11 12 13 14
p(x) 0.3 0.1 0.3 0.2 0.1
since the values that x can assume are mutually exclusive events, the event {x≤12} is the union of three mutually exclusive events, {x = 10}∪{x = 11}∪{x = 12}
...
c. find p(x≤14)
p(x≤14) = 1.0
d. find p(x = 14)
p(x = 14) = 0.1
e. find p(x≤11 or x > 12)
p(x≤11 or x > 12) = \square

Explanation:

Step1: Identify Mutually Exclusive Events

The events \( x \leq 11 \) and \( x > 12 \) are mutually exclusive (no overlap). So, \( P(x \leq 11 \text{ or } x > 12) = P(x \leq 11) + P(x > 12) \).

Step2: Calculate \( P(x \leq 11) \)

\( P(x \leq 11) = P(x = 10) + P(x = 11) = 0.3 + 0.1 = 0.4 \).

Step3: Calculate \( P(x > 12) \)

\( P(x > 12) = P(x = 13) + P(x = 14) = 0.2 + 0.1 = 0.3 \).

Step4: Sum the Probabilities

\( P(x \leq 11 \text{ or } x > 12) = 0.4 + 0.3 = 0.7 \).

Answer:

\( 0.7 \)