3 years ago
Suppose that X is a random variable with mean and variance both equal to 20. What can be said about P(0<X<40)?
1 Answers
Best Answer
beddle03 Staff answered 3 years ago
beddle03 Staff answered 3 years ago
Assume that X is a random variable with mean mu = 20
and variance sigma^(2)=20. Then, by Chebyshev's i not = uality,
P(|X-20|>= 20)<= (sigma^(2))/(20^(2))=(1)/(20).
Therefore, since P(|X-20|>= 20)=1-P(|X-20|<20), we have:
P(|X-20|<20)>= 1-(1)/(20)=(19)/(20). (*)
On the other hand,
P(|X-20|<20)=P(-20<X-20<20)=P(0<X<40)->^((*))
P(0<X<40)>= (19)/(20).
Result:
P(0<X<40)>= (19)/(20)