### Test 2

```Math 311
Test!
Fall 2013
(80 points)
Name:
.,
'
V
Every question is worth 4 points unless stated otherwise.
Parti: Probability
1. A die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its
faces, and the number 3 painted on one face. Assume that each face is equally likely to come up. What
is P[odd number]?
2. A system contains two components, A and B. The system will function so long as either A or B
functions. The probability that A functions is .95, the probability that B functions is .9, and the
probability that both function is .88. What is the probability that the system functions?
3. The probability of surviving a certain transplant operation is .55. If a patient survives the operation,
the probability that his or her body will not reject the transplant within one month is .8. What is the
probability of surviving both of these critical stages?
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4. The probability that a regularly scheduled flight departs on time is P[D] = .90, the probability that it
arrives on time is P[A] = .80, and the probability that it departs on time and arrives on time is
P [ Dn A ] = .72. Find the probability that a plane arrives on time given that it departs on time?
~~u
Part II: Discrete Functions
1. Suppose I have taught Math 175 (a fictional course) many times. Math 175 is a course that is taught
pass/fail, and over the years, I have noticed that 75% of my Math 175 students pass. If I teach Math
175 this coming spring semester and 13 people take the course,
a) what is Pfeveryone passes]?
b) what is P[less than 10 pass]?
c) what is u?
d) what is o2?
2. Computer chips often contain surface imperfections. For a certain type of computer chip, the
probability mass function of the number of defects X is presented in the following table.
X
P(x)
a) Find
P[X<2].
b) Find
c) Find n>.
d) Find
2
CT
0
0.4
1
0.3
2
0.2
3
0.1
3. A secretary makes 2 errors per page, on average. His/her errors have a poisson distribution. What is
the probability that on the next page he/she will make
a) 5 or more errors?
b) between 1 and 4 errors inclusively?
c) What is a2?
Part III: Continuous Functions
The pdf of the age of babies, x in years, being brought to a post natal clinic is given by
/(*)=
-(2x-x 2 )
0<jc<2
0
otherwise
a) WhatisP[0<X<l]?
~H
- o
b) WhatisE[X]?
c) What is Var[X]? (6 pts)
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>f \ 5
5
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5
A \ X * 4- -Ir
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Part IV: Other Stuff
Let E[X] = 4, E[X2] = 25, and Y = 2x - 5.
a) What is Var[X]?
b) WhatisE[Y]?
c) What is Var[Y]?
4
O^ A
```