Mean=Sum(X.P(X=x))=(1*0.1)+(2*0.2)+(3*0.1)+(4*0.3)+(5*0.2)+(6*0.1)

=0.1+0.4+0.3+1.2+1+0.6=3.6

Continuous uniform distribution is the one of the easiest continuous random variable and the probability density function f (x) of the continuous random variable X takes a constant value over the range of the random variable X is defined.

The standard normal curve is symmetric around the mean µ = 0. The standard normal distribution has a standard deviation ? = 1 of the distribution. The area under the standard normal distribution function for P (z ? 4.25) is approximately 1.

The answer is C.

We have to find the probabilty of getting 3 tails but no head. Thus the probabilty of TTT=(1/2)*(1/2)*(1/2)=1/8

The range of a data set, shown as R, is the difference between the largest and smallest values and calculated as follows: R = Largest Value - Smallest Value

Largest Value is 23

Smallest Value is 4 

So, R=23-4 = 19. 

The correct answer is B. 

Things measured by time, volume, length, height etc are type of contionus variables, but things meauser by numbers are discrete. However, number of students taking a course can be measured only in integers so it's a discrete variable.

For two dices the total number of possible outcomes is equal to 6*6 = 36. For the numbers' sum to be equal to 6 the number has to be (1,5), (2,4), (3,3), (4,2), (5,1) which shows that the number of times the event happening is equal to 5. The probability of two dices landing on numbers that when sum up is equal to 6 is 5/36. The answer is D.

A pretest over a small sample can help us in determining whether questions are clearly understood and whether the order of questions cause a difference in results.

Binomial distribution is a widely employed discrete probability distribution in statistics where a set of independent observations constitutes exactly two disjoint outcomes of a trial. Therefore in binomial distribution, an outcome of a random experiment can be classified under two different categories. For example, when a die is tossed once we observe six different numbers, that is x = 1, 2, 3, 4, 5 and 6. If we classified these outcomes as even or odd numbers then we will get two different outcomes. Likewise we can separate the turnover of a company into two categories, such as above and below the target level. Also, we can separate the exam grades simply into two categories, satisfactory and poor. The correct answer is A. 

Ux= E(X)=1.02+2.0,25+3.0,3+4.0,30=2,8

C(8, 3) * C(7, 2) + C(8, 2) * C(7, 3) . pg. 137. Correct answer is C.

According to the multiplication rule P(A?B) = P(A?B)*P(B). The values are given as P(B)=0.45 and P(A?B)=0.20. P(A?B) = (0.45)*(0.20) = 0.09. The answer is E.

25th percentile is the first quantile.

Exponential distribution is another most significant and extensively used continuous probability distribution. Exponential random variable is frequently used to model the time interval between two events. Some illustrations of random variables that generally conform to model by means of exponential
distribution are presented below.
• Arrival time between two customers.
• Time between two messages.
• Time between telephone calls received by a customer service.
• Time between customers who are arriving to the checkout lane of the supermarket.
• Time between two failures of a certain mechanical device.

To create a histogram for continuous data, the following steps may be used: 

1. Determine the sample size, 

2. Create the grouped frequency distribution of the data 

3. Include the relative frequency of each bin (class) to your grouped frequency distribution

4. Draw a rectangular for each bin.