 # Discrete probability distribution problems and solutions pdf

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## Constructing a probability distribution for random variable

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A continuous distribution describes the probabilities of the possible values of a continuous random variable. A continuous random variable is a random variable with a set of possible values known as the range that is infinite and uncountable.

Probabilities of continuous random variables X are defined as the area under the curve of its PDF. Thus, only ranges of values can have a nonzero probability. The probability that a continuous random variable equals some value is always zero. The continuous normal distribution can describe the distribution of weight of adult males. For example, you can calculate the probability that a man weighs between and pounds.

The shaded region under the curve in this example represents the range from and pounds. The area of this range is 0. The entire area under the curve equals 1. However, the probability that X is exactly equal to some value is always zero because the area under the curve at a single point, which has no width, is zero.

For example, the probability that a man weighs exactly pounds to infinite precision is zero. You could calculate a nonzero probability that a man weighs more than pounds, or less than pounds, or between A discrete distribution describes the probability of occurrence of each value of a discrete random variable. A discrete random variable is a random variable that has countable values, such as a list of non-negative integers. With a discrete probability distribution, each possible value of the discrete random variable can be associated with a non-zero probability.

Thus, a discrete probability distribution is often presented in tabular form. The shaded bars in this example represents the number of occurrences when the daily customer complaints is 15 or more.

The height of the bars sums to 0. Continuous and discrete probability distributions Learn more about Minitab. Probability distributions are either continuous probability distributions or discrete probability distributions, depending on whether they define probabilities for continuous or discrete variables. In This Topic What is a continuous distribution? What is a discrete distribution? What is a continuous distribution? Example of the distribution of weights The continuous normal distribution can describe the distribution of weight of adult males.

Distribution plot of the weight of adult males The shaded region under the curve in this example represents the range from and pounds. Example of the number of customer complaints With a discrete distribution, unlike with a continuous distribution, you can calculate the probability that X is exactly equal to some value.

For example, you can use the discrete Poisson distribution to describe the number of customer complaints within a day. Suppose the average number of complaints per day is 10 and you want to know the probability of receiving 5, 10, and 15 customer complaints in a day. You can also view a discrete distribution on a distribution plot to see the probabilities between ranges. Distribution plot of the number of customer complaints The shaded bars in this example represents the number of occurrences when the daily customer complaints is 15 or more.

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Compute the probability that the sum is even. Statistics and Probability with Applications High School. Reeve Assistant Editor It includes new problems, exercises, and text material chosen both for its inherent interest and for its use in building. Statistics Probability There are hundreds of problems available in the form of Strategic Practice and former Homeworks, all with complete solutions. Probability and Statistics 2-downloads. General Learning Outcome s : Collect, display, and analyze data to solve problems.

A discrete probability distribution function has two characteristics:. A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. X takes on the values 0, 1, 2, 3, 4, 5. This is a discrete PDF because:. A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a hour shift. examine two of the most important examples of discrete random variables: the of a discrete random variable and the associated probability distributions. Solution. The possible permutations are. ABCD ABDC ADBC ADCB ACBD ACDB.

### Constructing a probability distribution for random variable

In probability theory and statistics , a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. For instance, if X is used to denote the outcome of a coin toss "the experiment" , then the probability distribution of X would take the value 0. Examples of random phenomena include the weather condition in a future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc.

There are two types of random variables , discrete random variables and continuous random variables. The values of a discrete random variable are countable, which means the values are obtained by counting. All random variables we discussed in previous examples are discrete random variables. We counted the number of red balls, the number of heads, or the number of female children to get the corresponding random variable values. The values of a continuous random variable are uncountable, which means the values are not obtained by counting. A continuous random variable takes on an uncountably infinite number of possible values. We'll do that using a probability density function "p. We'll first motivate a p.

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