Hi! I really need help with this problem, if you could show work so I could foll

Question

Hi! I really need help with this problem, if you could show work so I could follow along I would greatly appreciate it! Thanks in advance!

1.3 A basket contains 4 puppies: one of the puppies has 1 spot, one of the puppies has 2 spots, and the remaining two puppies have 4 spots. Suppose tuo puppies are selected at random without replacement. Let the random variable X equal the total number of spots on the selected puppies. (a) Find the probability distribution of X. (b) Find the probability that the puppies have a total of 5 spots, i.e. find P(X -5. (c) Find the probability that the puppies have a total of 6 or more spots, ie. find P(X 26). (d) Find the probability that the puppies have 5 or fewer spots or 8 spots, i.e. find P(X s5 or x-8). (e) Given that the puppies have 6 or more spots, determine the probability that both puppies have 4 spots each (ie, 8 spots total), ie· find P(X-8 X 26). (f) On average, how many spots do we expect on the two selected puppies? (g) Compute 2-Var(X).

Explanation / Answer

a. If two puppies are selected at random, then the number of spots, denoted by rv X is as follows:

The sample space is as follows:

S: {12, 21, 14, 41, 24, 42, 44, 11, 22}

X=0 P(x=0)=0

X=1 P(x=1)=0

X=2 P(x=2)=1/9

X=3 P(x=3)=2/9

X=4 P(x=4)=1/9

X=5 P(x=5)=2/9

X=6 P(x=6)=2/9

X=7 P(x=7)=0

X=8 P(x=8)=1/9

Thus, number of total spots to be observed are

Rx={2,3,4,5,6,8}

The probability mass function is as follows:

Px(x)={P(X=x) if x=2,3,4,5,6,8

=0 otherwise

b. P(puppies has total of 5 spots)=# of favourable outcomes/total outcomes=2/9=0.2222

c. P(puppies has 6 or more spots)=#of favorable outcomes/total outcomes=3/9=0.3333

d. P(X<=5 or X=8)=6/9+1/9=0.7777

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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