Suppose the income (in tens of thousands of pesos) of employees at University
X can be approximated by a continuous distribution with density
f(x) =
(
2x2; if x � 2
0; if x < 2
Find the probability that a randomly chosen employee has an income between P30,000
and P50,000.
2. 9 pts.
(a) Determine the value of c so that the following function is a probability density
function (pdf):
f(x) =
8>>><
>>>:
15
64
+
x
64
; if 2 � x � 0
3
8
+ cx; if 0 < x � 3
0; otherwise
(b) Find P(1 � X � 1).
(c) Find F(x), the cumulative density function.
3. 12 pts. Let X be a standard normal random variable. Find the following:
(a) P(0 � X � 1:42)
(b) P(0:73 � X � 0)
(c) P(1:37 � X � 2:01)
(d) P(X � 1:13)
4. 5 pts. A fair die is tossed 180 times. Find