Question

There is an exam which contains 4 questions as follow:

I) 3 questions have four multiple choices a, b, c and d

II) only one question is true and false

Let XX denotes the number of correct answers for part (I) and YY denotes the number of correct answers in true/false part. Find the joint probability distribution function fX,Y(x,y

Answer 1

There is a test which contains

4 questions as follows:

I) 3 questions having four multiple choices a,b,c,d.

II) 1 true/false question.

X denotes the number of correct answers for part I and Y denotes the number of correct answers for part II.

X can take values 0,1,2, 3.

Now, the chance of getting an MCQ right is 1/4, and getting it wrong is 3/4.

So,

Now, the chance of getting a true/false question right, is 1/2.

So, Y can take values 0 and 1.

So,

Now, the MCQs and true/false questions each are independent of each other.

So, the joint probability mass function of X and Y is

Where,