a few probability problems

[ajones51]

If anyone could please help me with the following problems, that would be awesome, thanks. They are from Probability and Statistics for Engineering and the Sciences Jay Devore 6th Edition

74) Individual A has a red die and B has a green die (both fair). If they each roll until they obtain five "doubles" (1-1,.....,6-6), what is the pmf of X = the total number of times a die is rolled? What are E(X) and V(X)?
I realize that this is a negative binomial problem but I think that regular binomial must play a role in the question and i'm not exactly sure how to get the right answers.

7 Consider writing onto a coputer disk and then sending it through a certifies that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter lambda = 0.2.
a) What is the probability that a disk has exactly one missing pulse?
b) What is the probaiblity that a disk has at least two missing pulses?
c) If two disks are independently selected ,what is the probability that netiher contains a missing pulse?

 

[Denis]

Individual A has a red die and B has a green die (both fair). If they each roll until they obtain five "doubles" (1-1,.....,6-6), what is the pmf of X = the total number of times a die is rolled? What are E(X) and V(X)?

WHY all the rhetoric? Is it not simply:
How often must 2 fair dice be rolled so that 5 doubles are obtained?

Answer: 30

 

[ajones51]

re: questions

No, I don't think the die question is as simple as that. Since a negative binomial counts the number of failures whereas a normal binomial takes into account the successes, I think there is something that has to be done to combine these two into one expression that is needed to generate the pmf.

I managed to get the answer for 78) so I'm looking for help with question 74) the die problem. thanks

 

[pka]

74) Individual A has a red die and B has a green die (both fair). If they each roll until they obtain five "doubles" (1-1,.....,6-6), what is the pmf of X = the total number of times a die is rolled? What are E(X) and V(X)?
I realize that this is a negative binomial problem but I think that regular binomial must play a role in the question and i'm not exactly sure how to get the right answers.

Probability and Statistics for Engineering and the Sciences Jay Devore is good text book, but I think that the text by Larson&Marx is better on ‘the negative binomial distribution. The E(X)=r/p and V(X)=r(1-p)/p<SUP>2</SUP>, where r is the number of required successes and p is the probability of one success.

There is one thing to note about this problem, you need five doubles of any sort. That means outcomes can repeat. The probability of a double is 1/6. And r=5. So Dennis is correct with the answer 30.
Now what is V(X)?