To purchase a certain high-level weapon in Final Fantasy XII, you must collect a

Question

To purchase a certain high-level weapon in Final Fantasy XII, you must collect and sell specific kinds of loot either stolen or dropped from monsters. To acquire one of the best 2-handed swords in the game, called the Tournesol, you need an item called a Gemsteel; they can be found by fighting a Level 99 Red Chocobo (a large bird somewhat similar to an ostrich). Even with extensive grinding, the chocobo only has a 1/256 chance of showing up; although he does rarely show up, when he finally does, the gemsteel is almost guaranteed. I recorded many of my farming attempts of this bird and take a random sample of 10 attempts. Let X = the number of times the Level 99 Red Chocobo appears and n = the number of tries to find the bird = 10. (a) What is the name of this distribution? What is/are the parameter(s)? (b) What is the probability that in the next 10 tries to find the Level 99 Red Chocobo, he appears exactly one time? (c) What are the expected value, variance and standard deviation of the Level 99 Red Chocobo's appearance in the 10 attempts?

Explanation / Answer

Let X be the random variable that numb er of time the level 99 Red Chocobo appears.

a) Here X follows Binomial distribution with parameters n = 10, p = 1/256

The probability mass function of X is,

P(X=x) = (10 C x) * (1/256)^x * (1 - 1/256)^(10-x) , x=0,1,............n

where C is used for combination.

b) Now here we have to find P(X=1)

P(X=1) = (10 C 1) * (1/256)^1 * (1 - 1/256)^(10-1)

= 0.0377

c) Find expected value, variance, and standard deviation of X.

We know that in the Binomial distribution

expected value = np = 10*(1/256) = 0.0391

variance = npq where q=1-p

variance = 10*1/256*(1-1/256) = 0.0389

standard deviation = sqrt(variance) = sqrt(0.0389) = 0.1973

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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