我有一個大學的機率數學題 ><!急
for each of the following determine c so that the function can serve as the probability distribution of a random variable with the given range:
a. f(x)=c (5/x) for x=0,1,2,3,4,5
b. f(x)= cx^2 for x=1,2,3,...,k
c. f(x)= c(1/4)^x for x=1,2,3,.....
please steps by steps !
Answers & Comments
Verified answer
第1題
5c(1+(1/2)+(1/3)+(1/4)+(1/5))=1
(137/12)c=1
c=12/137
第2題
c(1^2+2^2+3^2+----+k^2)=1
c*(1/6)*k*(k+1)(2k+1)=1
c=6/[k*(k+1)*(2k+1)]
第3題
c*[(1/4)+(1/4)^2+(1/4)^3+--------]=1
c*{(1/4)/[1-(1/4)]}=1
c*(1/3)=1
c=3