Question

Suppose X is a continuous variable with the following probability density: f(x)={C(10−x)2,0, if 0

Answer 1

`C = 1/18`

Explanation:

Remember that for a probability density function

`\int_(-\infty)^(\infty ) f(x) dx = 1`

Since
`f(x) = 0` outside
`[0,2]` we would have that

`\int_(0)^(2) C(10-x) dx = 1`

Therefore

`18C = 1 \\C = 1/18`