# math

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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) =
(
2x􀀀2; 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

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