Distributions Flashcards
(11 cards)
If X~B(n, p) what are E(X) and Var(X)?
E(X) = np Var(X) = np(1-p)
What are the conditions for a binomial distribution?
- A fixed number of trials, n.
- Each trial should be success or failure.
- The trials are independent.
- The probability of success, p, at each trial is constant.
If X~Po(λ) then what is P(X=x)?
P(X=x) = e^-λ X λ^x/x!
If X~Po(λ) then what are E(X) and Var(X)?
E(X) = λ Var(X) = λ
When can a Binomial distribution be approximated to a Poisson distribution?
If n is large and p is small.
If X~ U[a, b], what is the p.d.f of X?
f(x) = {1/b-a, a
If X~ U[a, b] what are E(X) and Var(X)?
E(X) = a+b/2 Var(X) = (b-a)^2/12
If X~ U[a, b], what is the c.d.f?
{ 0, x<a>b}</a>
If X~B(n, p), what is P(X=x)?
P(X=x) = nCx X p^x X (1-p)^n-x
When can a Binomial distribution be approximated by a Normal distribution?
When n is large and p is close to 0.5. A continuity correction should be used.
When can a Poisson distribution be approximated by a Normal distribution?
When λ is large. A continuity correction should be used.
