Suppose odd numbers 1, 3, 5 with probability C and on each of the even numbers with probability 2C.

(a) Find C.

(b) Suppose that the die is tossed. Let X equal 1 if the result is an even number, and let it be 0 otherwise. Also, let Y equal 1 if the result is a number greater than three and let it be 0 otherwise. Find the joint probability mass function of X and Y. Suppose now that 12 independent tosses of the die are made.

(c) Find the probability that each of the six outcomes occurs exactly twice.

Question

Rollins

Mathematics

30 September, 05:17

Suppose odd numbers 1, 3, 5 with probability C and on each of the even numbers with probability 2C.

(a) Find C.

(b) Suppose that the die is tossed. Let X equal 1 if the result is an even number, and let it be 0 otherwise. Also, let Y equal 1 if the result is a number greater than three and let it be 0 otherwise. Find the joint probability mass function of X and Y. Suppose now that 12 independent tosses of the die are made.

(c) Find the probability that each of the six outcomes occurs exactly twice.

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Answers (1)

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Abram Knox · Answer 1

Step-by-step explanation:

a) Odd numbers if n then even numbers also n

Total prob = 1 gives 3c=1

c=1/3

b) X=1, if even and

0, if odd

Y = 1, if x >3 and

=0 otherwise

xy can take values as 0 or 1

xy = 1 if x even and y is greater than 3, or favorable outcomes are

4, 6.

xy = 1 if die shows 4 or 6

=0 if otherwise

Prob (xy) = 1/3, for xy = 1 and

= 2/3 for xy = 0

This is binomial since each trial is independent.

If 12 tosses are made then if we have binomial proba

with n = 12 and p = 1/3 for success