Q4. A student randomly guesses on multiple choice exam (and hence independence between each question can be assumed). There are five questions, each question has five options. Let XX be the random variable for the number of correct guesses.

1. Write the distribution for XX.

2. Determine the probability of answering exactly 3 questions correctly.

3. Determine the probability of answering at most 2 questions correctly.

4. Determine the mean and variance of XX.

Q5. Given two random variables: X,YX,Y. They have the following distribution:

P(X=1)=0.4P(X=1)=0.4,P(X=0)=0.2P(X=0)=0.2,P(X=1)=0.3P(X=1)=0.3,P(X=2)=0.1P(X=2)=0.1;

P(Y=1)=0.4P(Y=1)=0.4,P(Y=2)=0.2P(Y=2)=0.2,P(Y=3)=0.4P(Y=3)=0.4.

1. Find E(X),E(Y),V(X),V(Y)E(X),E(Y),V(X),V(Y).

2. Assume the correlation between X,YX,Y is 0.13, find E(5YX),V(2X+4Y).