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STAT 4705 TESTI 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 0.
(@) Find the total number of possible license plates.
(b) Ifa license plate is selected at random from all possible license plates,
find the probability that all 4 digits arc the same.
(©) _ Ifa license plate is selected at random from all possible license plates,
find the probability that the sum of the four digits is 2.
(@ Given that the sum of the four digits is 2, find the conditional probability
that at least one of the digits isa 1,
The amount of electricity used by a company in one day (in units of a thousand
KWE) is a random variable with the following density
fx-fe O<x<2
f=
0 otherwise.
(®) Find the cumulative distribution fimetion for this distribution,
(b) Find ihe probability that the amount used in a day exceeds one thousand
KWH.
(©) Find the expected amount used in a day.
‘The joint probability function f(x,y) of the number X of buses and the number Y
of tucks per signal cycle at e propased left tum lane is shown below
(@) Find POSEY > 3), the probability that the total number of buses and
trucks per cycle is at Jeast 3.
(&) Find E(X+Y), the expected total number of buses and trucks per cycle,
(©) Find the conditional probability fanetion of X given that Y=E.
A communications system will transmit words represented by n binary digits
which are each 0 or 1. ‘The probability of an error in transmitting a digit is .04.
Assume that etrors in different digits transmitted are independent.
(@) Find the probability of at least one error in a transmitted word consisting
of 2=10 binary digits.
(b) Find the expected number of errors in a word of n=10 binary digits.
{c) Suppose thut a message vonsists of 5 words each consisting of 10
binary digits. Find the probability that exactly one of the words has at
least one error.
