Fix µ R, > 0, and a pair (a, b) R 2 with 0 < a < b. Let X N (µ, ) be a normal RV

Question

Fix µ R, > 0, and a pair (a, b) R 2 with 0 < a < b. Let X N (µ, ) be a normal RV. Find P(X [b, a] [a, b]), i.e., the probability that X lies either in the interval [a, b] or its reflection [b, a]. Your answer should be expressed in terms of (z) P(Z z) (the CDF of the standard normal RV Z N (0, 1)) and the constants (µ, , a, b).

Fix Au E R, or 0, and a pair (a, b) E R2 with 0 a b. Let X N N(A, o) be a normal RV. Find POX E b, -al Ula, b), i.e., the probability that X lies either in the interval Da, b or its reflection I b, -a Your answer should be expressed in terms of (2) POZ S 2) (the CDF of the standard normal RV ZN N(0,1)) and the constants (A, o, a, b).

Explanation / Answer

we know that

z= (x-u)/

Za = (a=u)/

Zb  =(b-a)/

P(X [b, a] [a, b]) = P(Zb) - P(a) = F(Zb) - F(Za)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.