Question

Suppose that in an automatic filling process of oil in cans, the content of cans the content of cans in gallons is Y= 50 + X where x is a random variable with density f(x)=1-|x| when |x| ≤0 and 0 when|x| >0, in a lot of 100 cans how many will contain 50 gallons or more? What is the probability that a can will contain less than 49.5 gallons less than 49 gallons? Also find F(x).

Answer 1

We are given with the modulus function. Using that a modulus function cannot be negative, we will set up our function limits. After that, we will define our f(x). A can will contain less than 49.5 gallons less than 49 gallons is not a possible case because it must be at least 50 or more in any scenario. Thus, we will find our F(x).