Question

Consider the following three random variables:

a) a coin is repeatedly flipped

Let X= number of tails before the first head

b) a box contains 10 red and 6 white chips. 5 chips are drawn at rabdom from the box.

Let Y= the number of red chips drawn.

c) A weighted die is rolled 12 times.

Let W= the number of times a "4" is rolled

in each case, decide whether the random variable is binomial.

Answer 1

Binomial experiment conditions :

a) There is no fixed number of trials, trials occur until you get first head.

Hence a is not binomial variable.

b) Yes, it it Binomial random variable. There are 6 white and 10 red chips. Hence in each trial either red chip or white chip will come up with probability of red chip as 10/16 and that of white chip as 6/16.

5 trials are conducted and number of red chips are noted which can have outcomes 0,1, 2,3,4,5.

c)This is also a binomial random variable. There are fixed number of trials =12 and in one trial a 4 may come up or may not.