Question

Let X be a random number between 0 and 1 produced by a random number generator. The random number generator will spread its output uniformly (evenly) across the entire interval from 0 to 1. All numbers have an equal probability of being selected. Find the value of aa that makes the following probability statements true.

(a)  P(x≤a)=0.8
a=

(b)  P(x < a) = 0.25

a=

(c)  P(x≥a)=0.17
a=

(d)  P(x>a)=0.73
a=

(e)  P(0.15≤x≤a)=
a=

Answer 1

We would be looking at the first 4 parts here.

We are given the distribution here as:

The probabilities here are computed as:

Therefore a = 0.8 is the required value here.

Similar to the above part, here a = 0.25

Therefore a = 0.25 would be the required value here.

Therefore a = 0.83 is the required value here.

Therefore a = 0.27 is the required value here.