1.Correlation coefficient lies between

a) -infinity to infinity

b) 0 to 1

c) -1 to 0

d) -1 to 1

2.If the two regression lines are 5x+2y=16 and 9x+10y=48 , then find the mean of X and mean Y.

a) mean(x) = 2 and mean(y) = 3

b) mean(x) = 5 and mean(y)=0

c) mean(x)=mean(y)

d) mean(x)=3 and mean(y) =2

3.Which of these following data are negatively correlated?

a) X and Y are continuous RV with JPDF (,)=^((+)), ,>0 with the marginal pdf of X and Y are ()=^(), >0 and ()=^(), >0

b) X and Y are RV's with E(XY)=5.6, E(X)=2 and E(Y)=3

c) The amount of workout in gym vs the amount of fat change.

d) :15,200,30:56,47,900

4.Let X be the number of students that arrive at a dean room per hour. Students arrive at random and the average number of students per hour is constant.

3()=((())^2)4,(4).

a) 0.322

b) 0.439

c) 0.629

d) 0.489

5.The MGF of a binomial RV X is given below. Find P(x=1).

()=(0.85+0.15^)^33

a) 0.2730

b) 0.4444

c) 0.0273

d) 0.3423

6.If X~Binom(n,p) and Y~Binom(m,p) are two independent binomial RV's. Then find the variance of the binomial RV Z=3X-2Y.

a) p(1-p)(3n-2m)

b) p(1-p)(9n+4m)

c) p(1-p)(3n+2m)

d) p(1-p)(9n-4m)

7.A coffee machine dispenses a cappuccino made up of black coffee distributed normally with mean 120 mL and standard deviation 7 mL, and froth distributed normally with mean 28 mL and a standard deviation of 4.5 mL. The capacity of each cup is 135.5 mL. Find the probability that the cup will overflow.

a) 0.3422

b) 0.0665

c) 0.5000

d) 0.5684

8.The lengths of rods produced by a machine have mean 100 cm and standard deviation 15 cm. Find the probability that if 60 rods are randomly chosen from the machine, the mean length of the sample will be at least 105 cm.

a) 0.2969

b) 0.7894

c) 0.9628

d) 0.8676