Question

Suppose you choose a real number X from the interval [3,16] with the density function

f(x)=Cx,

where C is a constant.

a) Find C. Remember that if you integrate a density function over the entire sample space interval, you should get 1.


b) Find P(E), where E=[a,b] is a subinterval of [3,16]
(as a function of a and b ).


c) Find P(X>4)


d) Find P(X<14)


e) Find P(X^2−18X+56≥0)

Note: You can earn partial credit on this problem.

Answer 1

We would be looking at the first 4 parts here as:

a) The sum of all probabilities across the X range should be 1. Therefore we get here:

Therefore C = 2/247 is the required value of C here.

b) The probability here is computed as:

This is the required probability function here.

c) The probability here is computed as:

Therefore 0.9717 is the required probability here.

d) The probability here is computed as:

Therefore 0.7571 is the required probability here.