A statistician’s teenage daughter withdraws a certain amount of money X from an

Question

A statistician’s teenage daughter withdraws a certain amount of money X from an ATM every so often, using a method that is unknown to him: she randomly spins a circular wheel that is equally divided among four regions, each containing a specific dollar amount, as shown. Bank statements reveal that over the past n = 80 ATM transactions, $10 was withdrawn thirteen times, $20 sixteen times, $30 nineteen times, and $40 thirty-two times.

Suppose this process continues indefinitely. Construct a probability table, and calculate the expected amount withdrawn per transaction, and the variance 2. (Verify that, for this sample, s2 and 2 happen to be equal.). How do you make a probability table with this information?

Explanation / Answer

the frequency table with the probability table will be

x f(x) p(x)

$10 =13 13/80 = 0.162

$20 =16 16/80 = 0.2

$30 =19 19/80 = 0.237

$40 = 32 32/80 = 0.4

expected amount per transaction = E(X) = X1*P(X1)+X2*P(X2)+....+XN*P(XN)

= 10*0.162 + 20*0.2 + 30*0.237 + 40*0.4 = 28.73

VAR(X) = E(X^2) - E(X)^2

= 949.5 - 825.41 = 124.09

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