Question

A) Suppose we are considering a binomial random variable X with n trials and probability of success p.

Identify each of the following statements as either TRUE or FALSE.

a) False or True - The variance is greater than n.

b)    False or True - P(X=n)=pn.

c)    False or True - Each individual trial can have one of two possible outcomes.

d)    False or True - The largest value a binomial random variable can take is n + 1.

e) True or False - X can take a total of n possible values.

Answer 1

X Binomial random variable with n trails and probability of success : p

a) Variance of a binomial  distribution is npq

p and q are probabilities so they are from 0 to 1 . Therefore pq is less than or equal 1 ; therefore variance : npq is less than or equal n.

Variance greater than n is False.

b) False or True - P(X=n)=pn.

Probability mass function of a Binomial distribution:

i.e

False if P(X=n) = pn

True if P(X=n) = pⁿ

c)True - Each individual trail can have one of two possible outcomes

d) False - The largest value a binomial random variable can take is n + 1.

The possible values of X = 0,1,2,3,....n

The largest value a binomial random variable can take is n

e) False - X can take a total of n possible values.

The possible values of X = 0,1,2,3,....n

X can take a total of n+1 values [ 1,2,3,...n : constitute n values ; '0' another value; so a total of n+1]