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.

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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.

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What thoughts do you have about the truth or falsehood of each statement?

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Originally Posted by BDJ9189

Bump.

Can someone answer these please?

Thanks.

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Refer to question asked in post #2.

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 :(

Quote:

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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.

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(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