Question

Let X represent a continuous random variable with a Uniform distribution over the interval from 0 to 2. Find the following probabilities (use 2 decimal places for all answers): (a) P(X ≤ 1.92) = (b) P(X < 1.92) = (c) P(0.22 ≤ X ≤ 1.56) = (d) P(X < 0.22   or   X > 1.56) =

Answer 1

The interval space = 2 units

a) P(x1.92) = 1.92/the interval space = 1.92/2 = 0.96

b) p(X<1.92)

this can be interpreted as P(x1.92) - p(x=1.92)

But in a continuos distribution, the probability of x being exactly equal to 1.92 is 0

Therefore, p(X<1.92) = 0.96

c)p(0.22x1.56) = p(x1.56) - p(x0.22) = 0.78-0.11 = 0.67

d) P(x<0.22 or x>1.56) = p(x<0.22) + p(x>1.56)

We can get these values from the previous problem

p(x<0.22) + p(x>1.56) = 0.11 + (1-0.78) = 0.22+0.11 = 0.33