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}.
...
b. find p(x > 12).
p(x > 12) = 0.3
c. find p(x ≤ 14)
p(x ≤ 14) = 1.0
d. find p(x = 14)
p(x = 14) = \square

Explanation:

Step1: Identify the probability for x=14

From the given discrete probability distribution, the probability \( p(x) \) for \( x = 14 \) is directly provided in the table as \( 0.1 \).

Step2: Confirm the value

Since in a discrete probability distribution, \( P(x = 14) \) is equal to \( p(14) \), and from the table, \( p(14)=0.1 \).

Answer:

\( 0.1 \)