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STAT 4705 TEST I Feb. 16, 1996
Name _________ _
1. A campus license plate has 4 digits selected from 0,1,2, .... 9, where a digit may
be used more than once and the first digit may be O.
(a) Find the total number of possible license plates.
(b) If a license plate is selected at random from all possible license plates,
find the probability that all 4 digits are the same.
(c) If a license plate is selected at random from all possible license plates,
find the probability that the sum of the four digits is 2.
(d) Given that the sum of the four digits is 2, find the conditional probability
that at least one of the digits is a 1.
2. The amount of electricity used by a company in one day (in units of a thousand
KWH) is a random variable with the following density
~x) {-ix' :::
(a) Find the cumulative distribution function for this distribution.
(b) Find the probability that the amount used in a day exceeds one thousand
KWH.
(c) Find the expected amount used in a day.
3. The joint ...

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