# math

posted by
**vilma**
.

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 the probability P that the face 6 will

appear between 29 and 32 times inclusive.

1