Suppose X is a continuous random variable that is uniformly distributed between 3 and 8. Which one of the following functions can be used to find P(X<=5.8)?

Question

import scipy.stats as st

1-st.uniform.cdf(5.8,loc=3,scale=8)

import scipy.stats as st

st.uniform.cdf(5.8,loc=3,scale=5)

Answer 1

If this problem is supposed to be solved using a particular programming language, I can't help you. The answer is straightforward.

Solution 1:

(5.8 - 3)/(8 - 3) = 2.8/5 = .56

Solution 2:

If a distribution is uniform from 3 to 8, f(x) = 1/(8-3) = 1/5 on 3 <= x <= 8

Then, P(X <= 5.8) = 1/5(5.8-3) = 1/5(2.8) = .56

Solution 3:

If f(x) = .2 on 3 <= x <= 8,

F(x) = 0 x <= 3

.2(x - 3) = .2x - .6 3 <= x <= 8

1 x <= 8

Then, P(X <= 5.8) = F(5.8) = .2(5.8) - .6 = 1.16 - .6 = .56