Greg is preparing for an intercollegiate competition in discus. In each throw he

Question

Greg is preparing for an intercollegiate competition in discus. In each throw he gets a distance X that his friend Tom has shown to be uniformly distributed between 60 and 90 feet. Greg's goal is to get a throw of at least 80 feet. Each throw is known to be independent of other throws. What is the expected value of X? What is the probability that Greg succeeds in any single throw? Let the random variable K denote the number of throws up to and including the throw when he first achieves his goal. What is the expected value of K? Assume that on this particular day Greg keeps practicing until he has thrown the discus 10 times and then stops. Let M denote the number of times he achieves his goal in those 10 throws: What is the expected value of M? a) b) c) d)

Explanation / Answer

here as X has uniform distribution with parameter a =60 and b=90.

a) expected value of X =(a+b)/2 =(60+90)/2 =75

b) probability of throwing more then 80 feet in a single throw =P(X>80) =(90-80)/(90-60)=10/30=1/3

c)K has a geometric distribution with paramter ; probability of success p=1/3

hence expected value of k =1/p =1/(1/3) =3

d)here M has negative binomial distribution with paramter r =10 and p=1/3

therefore expected value of M =r/p =10/(1/3) =30

please revert for any clarification required,

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

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