Question

1.a

Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on the digits. What are the possible values of X?

1, 2, 3, 4

0, 1, 2, 3, 4, ...

0, 1, 2, 3, 4

0, 1, 2, 3

1, 2, 3, 4, ...

For the following possible outcomes, give their associated X values.

PIN associated

value

1107

2070

7177

1b. The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)

(a) T = the total number of pumps in use

T =

(b) X = the difference between the numbers in use at stations 1 and 2

X =

(c) U = the maximum number of pumps in use at either station

U =

(d) Z = the number of stations having exactly two pumps in use

Z =

1c. A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space along with the associated value of X.

S: FFF SFF FSF FFS FSS SFS SSF SSS

X:

Answer 1

Que.1

a.

Pin contains 4 digits, hence maximum numberof nonzero digits is 4 and minimum nonzero digit is 0.

Hence possible values of X are 0,1,2,3,4

X(1107) = 3

X(2070) = 2

X(7177) = 4

1b.

a.

T = Total number of pumps in use

There are total 6+4 = 10 pumps

Hence Possible values of T are 0, 1, 2, ----, 10

b.

X1 = number of pumps in use at station 1 = 0,1,----,6

X2 = number of pumps in use at station 2 = 0,1,----,4

Hence X = 0, 1, ----, 6

c.

U = 0, 1, -----, 6

d.

z = 0,1,2

1c

S	FFF	SFF	FSF	FFS	FSS	SFS	SSF	SSS
X	0	1	1	1	2	2	2	3