1.
Find the probability distribution and distribution function of the product , where
are the random variables for the two dice pips.
.
2. If one bronze coin is thrown and the face comes out, it is expressed as 1, and if the tail comes out, it is expressed as 0. When throwing three bronze coins, let be the random variables for the appearance of each bronze coin.
(1) Let . Then the domain of
is
.Also note that the probability distribution
is given by
.
First consider
.Since
,
It's the same as throwing two dice and finding the probability of both rolling one. The combination of both 1's pips is 1 out of 36 ways.Thus
.Similarly,we fin for
,
(2)
a Let
. Then the domain of
is
and the probabilty distribution
is given by
.
First consider .Since
,
It's the same as throwing three bronze coins and finding the probability that all of them will come out. All tails combinations are 1 out of 8.Thus
.Similarly we find for
,
b Find the distribution function . Since
,we have