binomial distribution

• Sep 3rd 2009, 02:47 AM
wik_chick88
binomial distribution
Which of the following statements concerning the binomial distribution are true?

(1) It is possible, for some parameter values, for the binomial distribution to have more than one modal value.
(2) For a given sample size, the variance of the binomial distribution is smallest when the probability of success is exactly 1/2.
(3) For a fixed probability of success, the binomial distribution becomes less symmetric on increasing the sample size.
(4) The probability of success is determined by the probability of failure and vice versa.
(5) The binomial distribution is completely specified by its parameters, n and p.
(6) The range of values that can be taken on by a binomial random variable is any integer value between 0 and n inclusive.
(7) The binomial distribution provides a listing of all possible collectively exhaustive, though not necessarily mutually exclusive, outcomes for the random variable it is modelling, such that a certain probability of occurrence is associated with each outcome.
• Sep 3rd 2009, 04:53 AM
mr fantastic
Quote:

Originally Posted by wik_chick88
Which of the following statements concerning the binomial distribution are true?

(1) It is possible, for some parameter values, for the binomial distribution to have more than one modal value.
(2) For a given sample size, the variance of the binomial distribution is smallest when the probability of success is exactly 1/2.
(3) For a fixed probability of success, the binomial distribution becomes less symmetric on increasing the sample size.
(4) The probability of success is determined by the probability of failure and vice versa.
(5) The binomial distribution is completely specified by its parameters, n and p.
(6) The range of values that can be taken on by a binomial random variable is any integer value between 0 and n inclusive.
(7) The binomial distribution provides a listing of all possible collectively exhaustive, though not necessarily mutually exclusive, outcomes for the random variable it is modelling, such that a certain probability of occurrence is associated with each outcome.

What thoughts do you have about the truth or falsehood of each statement?
• Apr 20th 2010, 06:54 PM
mr fantastic
Quote:

Originally Posted by BDJ9189
Bump.

Thanks.

Refer to question asked in post #2.
• Apr 20th 2010, 07:11 PM
BDJ9189
1) True?
2)True. less spread due to 50/50?
3)Faluse. if p(success) is fixed it should remain symmetrical
4)True. 1-p(Failure) = p(success)
5)Faulse. doesnt account for x
6)True. needs to be whole number?
7)True?

I suck at binomials :(
• Apr 21st 2010, 06:56 PM
mr fantastic
Quote:

Originally Posted by wik_chick88
Which of the following statements concerning the binomial distribution are true?

(1) It is possible, for some parameter values, for the binomial distribution to have more than one modal value.
(2) For a given sample size, the variance of the binomial distribution is smallest when the probability of success is exactly 1/2.
(3) For a fixed probability of success, the binomial distribution becomes less symmetric on increasing the sample size.
(4) The probability of success is determined by the probability of failure and vice versa.
(5) The binomial distribution is completely specified by its parameters, n and p.
(6) The range of values that can be taken on by a binomial random variable is any integer value between 0 and n inclusive.
(7) The binomial distribution provides a listing of all possible collectively exhaustive, though not necessarily mutually exclusive, outcomes for the random variable it is modelling, such that a certain probability of occurrence is associated with each outcome.

(1) True eg. n = 3, p = 1/2.
(2) False. Variance is largest when p = 1/2.
(3) F
(4) T
(5) T
(6) T
(7) F