(1 point) The problem below describes an experiment and defines a random variabl

Question

(1 point) The problem below describes an experiment and defines a random variable. (a) Find the distribution of the random variable (and provide it as a chart). (b) Calculate the expected value of the random variable. A certain brand of trading cards is available in smaller packs that cost $2 each. Assume that any given pack has a 10% chance of containing a rare card, independently of other packs. Alice will buy and open a pack until she gets a rare card, but she will not buy more than five. Let M be the amount of money (in dollars) that Alice will spend. P(m) (b) Expected Value

Explanation / Answer

a) For m = 1: P(m) = 0.10

For m = 2: P(m) = (0.90)*(0.10) = 0.09

For m = 3: P(m) = (0.90)2 * (0.10) = 0.081

For m = 4: P(m) = (0.90)3 * (0.10) = 0.0729

For m = 5: P(m) = (0.90)4 * (0.10) = 0.06561

Hence,

The table will be:

b) Expected value = 1(0.10) + 2(0.09) + 3(0.081) + 4(0.0729) + 5(0.06561) = 1.14265

m 1 2 3 4 5 P(m) 0.10 0.09 0.081 0.0729 0.06561

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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