Question

1. Determine whether or not the random variable X is a binomial randon variable. If so give the values of n and p. If not, explain why not. a. X is the number of dots on the top face of fair die that is rolled. b. X is the number of hearts in a five-card hand drawn (without replacement) from a well-shuffled ordinary deck c. X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process ii which 0.02% of all parts are defective. d. X is the number of times the number of dots on the top face of a fair die is even rolls of the die in Xis the number of dice that show an even number of dots on the top face when e SIX dice are rolled at once.

Answer 1

For a random variable to be binomial:

1. Observations are independent

2. The probability remains the same in each trial

3. Two exclusive outcomes

a) There are 6 outcomes in this case.

This is not binomial.

b) The probability of drawing a heart does not remain the same and depend upon previous outcome

This is not binomial.

c) This is the case of binomial

d) This is the case of binomial

e) This is the case of binomial