Homework SourseA computer terminal can pick up erroneous signal from the ke
A computer terminal can pick up erroneous signal from the keyboard that does not show up on the screen. this creates a silent error difficult to detect. assume that for a particular keyboard, the probability that this will occur per entry is 1/1000. let X be the number of silent errors in 12000 entries.
a) what is the distribution of X? E(X)?
B) what distribution can be used to approximate X. use this distribution to find the probability of at least one silent error.
A computer terminal can pick up erroneous signal from the keyboard that does not show up on the screen. this creates a silent error difficult to detect. assume that for a particular keyboard, the probability that this will occur per entry is 1/1000. let X be the number of silent errors in 12000 entries.
a) what is the distribution of X? E(X)?
B) what distribution can be used to approximate X. use this distribution to find the probability of at least one silent error.
A computer terminal can pick up erroneous signal from the keyboard that does not show up on the screen. this creates a silent error difficult to detect. assume that for a particular keyboard, the probability that this will occur per entry is 1/1000. let X be the number of silent errors in 12000 entries.
a) what is the distribution of X? E(X)?
B) what distribution can be used to approximate X. use this distribution to find the probability of at least one silent error.
Solution
X is the number of silent errors in 12000 entries.
the probability of silent error per entry is 1/1000
a) here X~Bin(12000,1/1000)
so E[X]=12000*1/1000=12
b)as here n=12000 is a very large number and p=0.001 is very low.
hence X can be approximated by a poisson distribution with mean=12000*0.001=12
so X~P(12)
now P[X>=1]=1-P[X<1]=1-P[X=0]=1-0.0000061=0.9999939 [answer]
