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butalik [34]
3 years ago
14

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​
Mathematics
1 answer:
wariber [46]3 years ago
8 0

Answer:

The expected value of lateness \frac{7}{20} 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:

E(X)=\sum x\cdot P(X=x)

Compute the expected value of lateness as follows:

E(X)=\sum x\cdot P(X=x)

         =(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}

Thus, the expected value of lateness \frac{7}{20} hours.

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