Question is not well presented.
Full Question
Suppose the cumulative distribution function of the random variable X is F(x) = 0.25x + 0.4
For {0, x < -1.6; -1.6 ≤ x ≤ 2.4; 1, x ≥ 2.4}
(Round your answers to 3 decimal places) Determine the following:
1. P(X < 1.8)
2. P(X> - 1.5)
3. P(X < - 2)
Answer:
1. P(X<1.8) = 0.85
2. P(X> - 1.5) = 0.975
3. P(X < - 2) = 0
Step-by-step explanation:
1. Calculating P(X < 1.8);
Since, F(x) = 0.25x + 0.4
P(X<1.8) = 0.25(1.8) + 0.4
P(X<1.8) = 0.85 or 85%
2. Calculating P(X> - 1.5)
Here
P(X> - 1.5) + P(X≤-1.5) = 1
P(X> - 1.5) = 1 - P(X≤-1.5)
Calculating P(X≤-1.5)
P(X≤-1.5) = 0.25(-1.5) + 0.4
P(X≤-1.5) = 0.025
So,
P(X> - 1.5) = 1 - 0.025
P(X> - 1.5) = 0.975
3. Calculating P(X < - 2)
X < -2 doesn't fall within the range of values given in (question) above.
So, P(X < - 2) = 0
