Disks of polycarbonate plastic from a supplier are analyzed

Probability And Statics Work

Homework #1

Name: _______________________________

1. Three attempts are made to read data in a magnetic storage device before an error recovery procedure that repositions the magnetic head is used. The error recovery procedure attempts three repositioning before an “abort’’ message is

sent to the operator. Let

s denote the success of a read operation f denote the failure of a read operation

S denote the success of an error recovery procedure

F denote the failure of an error recovery procedure A denote an abort message sent to the operator

Describe the sample space of this experiment with a tree diagram.

2. In the layout of a printed circuit board for an electronic product, 12 different locations can accommodate chips.

(a) If five different types of chips are to be placed on the board, how many different layouts are possible?

(b) If the five chips that are placed on the board are of the same type, how many different layouts are possible?

3. Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:

Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch

resistance. If a disk is selected at random, determine the following probabilities:

(a) P(A) 

(b) P(B) 

(c) P(A')  

(d) P(AB) 

(e) P(AB) 

(f) P(A’B)

4. Samples of skin experiencing desquamation are analyzed for both moisture and melanin content. The results from 100 skin samples are as follows:

Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content. Determine the following probabilities:

(a) PA  

(b) PB  

(c) PA | B 

(d) PB | A

5. A lot of 100 semiconductor chips contains 20 that are defective.

(a) Two are selected, at random, without replacement, from the lot. Determine the probability that the second chip selected is defective.

(b) Three are selected, at random, without replacement, from the lot. Determine the probability that all are defective.

6. The following circuit operates if and only if there is a path of functional devices from left to right. The probability that each device functions is as shown. Assume that the probability that a device is functional does not depend on whether

or not other devices are functional. What is the probability that the circuit operates?

7. A visual inspection of a location on wafers from a semiconductor manufacturing process resulted in the following

table

Number of Contamination particles Proportion of wafers

1 0.40

2 0.20

3 0.10

4 0.05

5 or more 0.10

Assume wafers are independent with respect to contamination particles. Wafers are selected until one with 5 or more contamination particles occurs what is the probability mass function of the number X of wafers selected.

8. Calculate the mean and variance for the random variable in the previous problem.