3. From the table below, find Prof. Xin expected value of lateness. (5 points) Lateness P(Lateness) On Time 4/5 1 Hour Late 1/10 2 Hours Late 1/20 3 Hours Late 1/20​

Answers

Answer 1

Answer:

The expected value of lateness [tex]\frac{7}{20}[/tex] hours.

Step-by-step explanation:

The probability distribution of lateness is as follows:

  Lateness             P (Lateness)

  On Time                     4/5

1 Hour Late                  1/10

2 Hours Late                1/20

3 Hours Late                1/20​

The formula of expected value of a random variable is:

[tex]E(X)=\sum x\cdot P(X=x)[/tex]

Compute the expected value of lateness as follows:

[tex]E(X)=\sum x\cdot P(X=x)[/tex]

         [tex]=(0\times \frac{4}{5})+(1\times \frac{1}{10})+(2\times \frac{1}{20})+(3\times \frac{1}{20})\\\\=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20}\\\\=\frac{2+2+3}{20}\\\\=\frac{7}{20}[/tex]

Thus, the expected value of lateness [tex]\frac{7}{20}[/tex] hours.

Answer 2

An expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment.

Expected value of lateness is  [tex]\frac{7}{20}[/tex] hours.

Let us consider, P(x) is represent that probability of lateness and x represent number of hours late.

So, below a table is formed.

         x       0             1            2           3

      P(x)      4/5         1/10      1/20       1/20

From formula of expected value,

        E(x) = ∑ x P(x)

[tex]E(x)=(0*\frac{4}{5} )+(1*\frac{1}{10} )+(2*\frac{1}{20} )+(3*\frac{1}{20} )\\\\E(x)=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20} \\\\E(x)=\frac{7}{20}[/tex]

So, expected value of lateness is 7/20 hours.

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Related Questions

Can someone help me? Please i need this done

Answers

Your answer is y=-10x+8b I think. This is because on the x axis it hits -10 and on the y axis it’s 8

2)
Mike went to the doctor and was found to be 20 pounds overweight.
The doctor discovered that Mike ate an average of 2000 calories per
day. He said for Mike to lose weight and meet his goal, the maximum
amount of calories he could eat per day was 1750. How many calories
will Mike be cutting out each week (7 days)?

Answers

Answer:

1750 Calories

Step-by-step explanation:

2000-1750=250

250x7=1750

How do you get from one number to the next using multiplication or division?
From 100 to 106
From 100 to 90
From 90 to 100
From 106 to 100

Answers

Answer:

You use decimal values. Like for the first one, multiply 100 by 0.01.

Step-by-step explanation:

The multiplication or division is 10^6/10^4

How to interpret integral multiplication?

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b

Then, their multiplication can be interpreted as:

[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]

For example,

[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]

Given;

From 100 to 10^6;

100 * 10^4  = 10^6

From 100 to 90;

100/10*9=90

From 90 to 100

90/9*10=100

From 10^6 to 100

10^6/10^4=100

Therefore, by multiplication or division will be 10^6/10^4

Learn more about multiplication here:

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