You randomly choose cookies from a very large container. Assume that 35% of the

Question

You randomly choose cookies from a very large container. Assume that 35% of the cookies are chocolate chip and 65% of the cookies are not chocolate. Assume that your selections of cookies are independent, and assume that the container is so large that these percentages do not change with each subsequent draw. (If you prefer, you can just sample the cookies with replacement, but nobody likes to put cookies back!) Let X denote the number of chocolate chip cookies that you get, when you choose 5 cookies from the cookie jar.

a. Suppose that your brother also chooses 5 cookies, and let Y denote the number of chocolate chip cookies that he gets. Assume that X and Y are independent. Define W=X+Y. Is W a Binomial random variable? (and Why?)

If “Yes", what are the parameters n and p for the random variable W?
(Put 0 if you don't think W is a random variable.)

n=

p=

b. Is U=2X?Y a Binomial random variable? (and why?)

If “Yes", what are the parameters n and p for the random variable U?
(Put 0 if you don't think U is a random variable.)

n=

p=

Explanation / Answer

(a) Yes ,

W is a binomial random variable

Because sum of two binomial variate with parameter n1 and n2 with common probability p is a binomial variate

With parameters n= n1+ n2 and p

n= 10

p = 0.35

(b) 0

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