Question
10. What is the probability density of the sum of two independent random variables, each of...
10. What is the probability density of the sum of two independent random variables, each of which is uniformly distributed over the interval 0, 1]?
Answers
Let x 4nd Y be amton vaeiables decoibing oue chaises and, Xt theiesum. We have, )y 1ioz qnd the densihy uncion for the sum is given by, t ) dy Since, fr() = 1 )= J(-9) dy -CO 6 otherwise. inlegrand tso unless ozスーy(1(ieunless ズ-1<4く) Noo the and then it is 1 so, }z) dy When, z2 then fe)= dy = 2-z it oZ We have, Z 1 theny it o<z£i 2-z itt< z< 2 O
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