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}
...
a. find p(x≤12)
p(x≤12) = 0.7
b. find p(x > 12)
p(x > 12) = 0.3
c. find p(x≤14)
p(x≤14) = □

Explanation:

Step1: Recall Probability of Discrete RV

For a discrete random variable, the sum of all probabilities is 1, and \( P(x \leq 14) \) is the sum of probabilities for \( x = 10, 11, 12, 13, 14 \).

Step2: Sum the Probabilities

Add \( p(10) = 0.3 \), \( p(11) = 0.1 \), \( p(12) = 0.3 \), \( p(13) = 0.2 \), \( p(14) = 0.1 \).
\( P(x \leq 14) = 0.3 + 0.1 + 0.3 + 0.2 + 0.1 \)

Step3: Calculate the Sum

\( 0.3 + 0.1 = 0.4 \); \( 0.4 + 0.3 = 0.7 \); \( 0.7 + 0.2 = 0.9 \); \( 0.9 + 0.1 = 1.0 \).

Answer:

\( 1.0 \)