A recent study of 500 American males aged 18-21 found that 237 had 1 ticket in the past year, 112 had 2 tickets in the past year, 17 had 3 tickets in the past year, 5 had 4 tickets in the past year, and 1 had 5 tickets in the past year. The rest of the men did not have any tickets in the past year. What is the expected number of tickets an 18-21-year-old American male will have in one year?

The expected number of tickets is 1.273

Step-by-step explanation:

Expected Value of a Discrete Probability Distribution

Given a discrete distribution with values

x={x1,x2,x3,...,xn}

And respective probabilities

p={p1,p2,p3,...pn}

The expected value EX of the entire distribution is

The recent study of American males provides an approximate distribution of probabilities based on the number of tickets they had past year, according to the following data:

237 had 1 ticket

112 had 2 tickets

17 had 3 tickets

5 had 4 tickets

1 had 5 tickets

The total number of tickets is 237+112+17+5+1=372

Taking the number of tickets as the independent variable, then

x={1,2,3,4,5}

Each probability can be found as the relative frequency of the number of tickets as follows:

Therefore

p={0.637,0.301,0.046,0.013,0.003}

Compute EX

The expected number of tickets is 1.273