Which of the following statement (s) is/are true? No justification needed. I. Th

Question

Which of the following statement (s) is/are true? No justification needed. I. The smallest value a geometric random variable can possibly take is 0 II. The smallest value a Poisson random variable can possibly take is 0. III. The largest value a binomial random variable with parameters (n,p) can possibly take is n - 1. IV. The smallest value a binomial random variable with parameters (n, p) can possibly take is 1 V. If X ~ Bern(p) then P(X 0) p yl. If X ~ Geom(p) then P(X n)-(1-p)n-1 for all integer n > 1.

Explanation / Answer

I) The given statement here is FALSE because the geometric random variable is only defined for positive integers that is for X = 1, 2, 3, ......

II) The given statement here is TRUE because the poisson random variable is defined for non negative integers that is for X = 0, 1, 2, 3, ..........

III) Here we are given the distribution as: X = Bin(n, p )

Therefore X would be defined here for X = 0, 1, 2, ..... n

Therefore the maximum value for X here would be m and not ( n - 1 )

Therefore the given statement here is FALSE

IV) Here we are given the distribution as: X = Bin(n, p )

Therefore X would be defined here for X = 0, 1, 2, ..... n

Therefore the minimum value for X here would be 0 and not 1

Therefore the given statement here is FALSE

V) If we have X = Bern(p) . This means that:

P(X = 1) = p and P(X = 0) = 1 -p

Therefore the given statement here is FALSE

VI) Here we are given that X = Geom(p)

Therefore,

P(X > = n) = P(X > n-1 ) is computed as: (1 -p ) n -1

Therefore the given statement here is TRUE

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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