This is a permutation with  repeated items. If all the seven letters in the given word were different, the total number of arrangements would be 6!. Since all the arrangements of the two letters C1 and C2 , and all the arrangements of the two letters M1 and M2 should be counted only once, it follows that the answer is: 6!/2!2!=180

If this is a probabilty distribution than the sum of all probabilities must be equal to 1. Thus 0.2+0.3+0.1+a+b=1 which means a+b=0.4, thus b=0.4-a. Also it is given that the mean of X is equal to 2.8.

Mean=Sum((X=x)P(X=x))

2.8=(1*0.2)+(2*0.3)+(3*0.1)+(4*a)+(5*b)

2.8=1.1+4a+5b

1.7=4a+5b=4a+5(0.4-a)

1.7=2-a

0.3=a

Each dice has a possible outcome of 6 in total {1,2,3,4,5,6}. If they are thrown at the same time the possible outcome would equal to 6*6 = 36. The answer is D.

Int(25, 35)(f(x) dx) = 0.04 * x = 0.04 x (35 – 25) = 0.04 * 10 = 0.4. pg. 180. Correct answer is C.

z = (x – m) / sd ; (210 – 270) / 90 = -2/3 ; P(z <= (-2/3)) = P(z >= 2/3) = 0.5 – P(z = 2/3) . pg. 200. Correct answer is B.

Grades like "AA" or "BB" taken from a course is an ordinal categorical variable.

Discrete random variables have only a countable number of separate values such as 0, 1, 2 , 3... etc. For example, the number of students in a class for certain day or the number of customers in a supermarket after 5:00 PM are cases for discrete random variables since these variables are finite and countable. Conversely, continuous random variable can take entire infinite values in a given interval. Because of this reason, continuous random variables are commonly measured instead of counted. For instance, waiting time for customers in a supermarket cashier line and travel time of a bus between two points are examples for continuous random variables. The correct answer is D.

The sum of all probabilities must be equal to 1, if it is a probability distribution table. Thus 3k+5k+8k+3k+k=20k=1 then k=1/20=0.05

I. The exponential random variable is frequently used to model the time interval between two events. (True)

II. The exponential random variable is defined with a parameter ?. (True)

III. The exponential random variable X defines the time interval between two independent events. (False, the exponential random variable X defines the time interval between two consecutive events.)

The answer is C.

P(A)=0.40  P(U/A)=0.10  P(U/A).P(A)=0.04

P(B)=0.35  P(U/B)=0.20  P(U/B).P(B)=0.07

P(C)=0.25  P(U/C)=0.05  P(U/C).P(C)=0.0125

P(U)= 0,04+0,07+0,0125=0,12

P(A/U)=0,04/0,12=0,33

You get the mean score if you divide the total scores by the number of scores.So the correct answer is D.

When order is important, we call the arrangements of a finite number of distinct objects a permutation. For example, there are a total of 3!=6 different ordered arrangements of the three letters A,B, and C. If there are four letters (W,X,Y,Z) there are a total of 4!=24 different ordered arrangements.

0,01