Answer:
a. P(X>3000) = 0.062
b. P(1000 > X > 2000) = 0.239
c. P(X<1000) = 0.605
Step-by-step explanation:
Given
The General Probability Density Function of the random variable is is given as follows:
f(x) = e^-(x/1076)/1076 for x >0
To calculate the probability, we make use of
P(a<X<b) = 1/1076 ∫ e^-(x/1076) dx {b,a}
P(a<X<b) = e^-(x/1076) {b,a}
P(a<X<b) = e^-(a/1076) - e^-(b/1076)
a. P(X>3000)
This translates to
P(∞ > X > 3000)
= e^-(3000/1076) - e^-(∞/1076)
= e^-(3000/1076) - 0
= e^-(3000/1076)
= 0.061537773515010
= 0.062
b.
P(1000 > X > 2000)
= e^-(1000/1076) - e^-(2000/1076)
= 0.238933619675996
= 0.239
c.P(X<1000)
This translates to
P(0 > X > 1000)
= e^-(0/1076) - e^-(1000/1076)
= 0.605196864611088
= 0.605