I need two comments, each part is around 150 words.

Part 1:

Probability is the concept of how likely an event is to occur, based on a given set of conditions. Measuring the likelihood of an event is either Discrete or Continuous, and is done through the use of Probability Distributions. Discrete Probability Distributions contain data that can take on a finite number of values, whereas the data in Continuous Probability Distributions can represent an infinite number of values within a given range.

An example of a Discrete Probability Distribution is the set of values that are generated as a result of rolling a dice. We know that there are only six (6) possible values that a dice roll can generate, which include 0, 1, 2, 3, 4, 5, and 6. For example, we cannot roll 1.5 on a dice roll, as that would be classified as a Continuous Probability Distribution, which we would be discussing next.

On the other hand, a person’s weight can be an example of a Continuous Probability Distribution. This variable can contain a value that can range from 0 to an uncountable, infinite number of possible outcomes. Since weight can have a variety of decimal places and does not have a maximum value within its range, it cannot be termed as being a Discrete Probability Distribution.

With several other real-world examples that exist in our world today, the likelihood of Discrete and Continuous events is always being studied. Therefore, the probability of any given event must be classified appropriately – as either a Discrete or a Continuous Probability Distribution. By understand the difference between the two (2) types, we can design our experimental studies, which leverage well-informed, data-driven insights and generate the greatest impact across society.

Part 2:

1. A discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. The probabilities are determined theoretically or by observation (Bluman, 2018). In real life, we can use discrete distributions to predict the weather. For example, if 56% of the days in Pittsburgh in a year are cloudy (National Climatic Data Center), then we can calculate the relevant information about the number of cloudy days in the city in June.

The expected value of a discrete random variable of a probability distribution is the theoretical average of the variable. The formula is μ = E(X) = ΣX · P(X) = np (Bluman, 2018). Standard deviation, which is denoted by σ measures how spread out the value of the variable is. Therefore, calculating the average can help us predict the number of cloudy days in June, and the standard deviation can determine the distribution range of the number of cloudy days. In this example, there are 30 days in June, n=30, p=0.56, q=0.44, the mean and standard deviation are as follows:

μ = np = 30 * 0.56 = 16.8,

σ = √n p q = 2.7

Therefore, on average, 16.8 days are cloudy in June, with a standard deviation of 2.7 days. Deviations from the mean by more than two standard deviations are considered small probabilities.

16.8 – 2*2.7 = 11.4, so there is a small probability of 11 cloudy days in June.

Similarly, 16.8 + 2*2.7 = 22.2, there is a small probability that there will be 23 cloudy days in June.

2. The normal distribution is a continuous probability distribution. If a random variable has a probability distribution whose graph is continuous, bell-shaped, and symmetric, it is called a normal distribution (Bluman, 2018). For weight loss drug companies, a continuous normal distribution can calculate the probability of different degrees of weight loss after taking the product. For example, with this model, we can calculate the population distribution with an average weight loss of less than 10 pounds, greater than 20 pounds, or between 10 and 20 pounds.

In a continuous distribution, the mean or the expected value, denoted by µ is defined by the density curve of the distribution (Bluman, 2018). If it is a normal distribution curve, then the mean would lie in the center of the curve. In this example, the probability of weight loss is within a range of values and the mean of a random variable (weight loss) is a measure of the center of the distribution. Also, the standard deviation for a continuous distribution would be the measure of the horizontal spread/ dispersion of the random variable (which in this case is the weight lost between 10 and 20 pounds). A continuous random distribution can be used to test out the effectiveness of weight loss drug. The mean in this case would help us find out the probability of people who lost between 10 and 20 pounds of weight. Similarly, the standard deviation will help to find out the spread of those that lost weight between 10 and 20 pounds.