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An electrical unit consists of four components each of which is subject to failure

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An electrical unit consists of four components each of which is subject to failure.  Suppose that, at a specified time, we observe this unit to determine which components are working and which have failed.  Write the sample space associated with this random experiment.

 

 

2. Let S={0, 1, 2, 3, 4,  …}

   

   , A=

   

    the set of natural numbers divisible by 2

   

   , and B=

   

    the set of natural numbers divisible by 4

   

   .  What is the set A∩B

   

   ?  What is the set A∪B

   

   ?

 

 

3. In a certain residential suburb 60%

   

    of all households subscribe to the metropolitan newspaper, 70%

   

    subscribe to the local paper, and 40%

   

    to both newspapers.  What proportion of households does not subscribe to either one of the two newspapers?

 

 

4. There are seven different locations in which a switch can be added to a circuit.  If four different switches are to be placed in the circuit, how many different designs are there?  

 

 

 

5. In how many ways a sample containing 8

   

    non-defective and 2

   

    defective part can be chosen from a group containing 22

   

    non-defective and 7

   

    defective parts? 

 

6. How many barcodes can be formed using five a

   

   ’s, four b

   

   ’s and seven c

   

   ’s?

 

R questions

 

1. Compute 127!/91!

   

 

2. Construct a data frame whose first column consists of the numbers 1, …, 10, second column 3, …., 12, and the third column letters a, …,j.

 

3. Write the function

f(x)=x2x2+1

 

 

Then graph it over the interval [-3, 3].

 

4. Write the function

w=logx+yz

 

Compute w(17.5,23.7,19.8)

.

 

 

 

The center thickness (in mils) of a sample of twenty-five contact lenses are given below

0.3978                   0.4019                   0.4031                   0.4044                   0.3984                   0.3972                   0.3981  

0.3947                   0.4012                   0.4043                   0.4051                   0.4016                   0.3994                   0.3999

0.4062                   0.4048                   0.4071                   0.4015                   0.3991                   0.4021                   0.4009

0.3988                   0.3994                   0.4016                   0.4010

 

Using this data set and RStudio answer the five following questions

 

                Determine the mean, the standard deviation, the variance, and the five-number summary

 

                Using the fence rule, determine if data set has any outliers.

 

                Draw a histogram. Properly name the graph and the axes.

 

                Draw a boxplot (horizontal).

 

                Construct a qqplot and a qqline and determine if this data set is approximately normal.

 

 

                To experimentally verify the central limit theorem, take 1000 random samples of size n=33 from a population that is distributed  exponentially with λ=3.  To this end, you must show

 

                The histogram of the distribution is approximately normal. 

                Its expected value is μ.

                Its variance is σ^2/33.