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A insurance office keeps track of the number of car insurance claims filed each day. Based on the data collected, it determines that the following probability distribution applies: Number of Claims Probability 0 .25 1 .15 2 .25 3 .25 4 .10 a. What is the expected number of new claims filed each day

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Answer:

The expected number of new claims filed each day is 1.8.

Step-by-step explanation:

We are given the following probability distribution:

[tex]P(X = 0) = 0.25[/tex]

[tex]P(X = 1) = 0.15[/tex]

[tex]P(X = 2) = 0.25[/tex]

[tex]P(X = 3) = 0.25[/tex]

[tex]P(X = 4) = 0.1[/tex]

a. What is the expected number of new claims filed each day

Multiplication of each outcome by its probability, so:

[tex]E(X) = 0*0.25 + 1*0.15 + 2*0.25 + 3*0.25 + 4*0.1 = 1.8[/tex]

The expected number of new claims filed each day is 1.8.

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