ollege students are randomly selected in groups of three, the random variable x is the number in the group who say that they take one or more online courses. Determine ether a probability distribution is given. If a probability distribution is given find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied does the table show a probability distribution
ollege students are randomly selected in groups of three, the random variable x is the number in the group who say that they take one or more online courses. Determine ether a probability distribution is given. If a probability distribution is given find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied does the table show a probability distribution
ollege students are randomly selected in groups of three, the random variable x is the number in the group who say that they take one or more online courses. Determine ether a probability distribution is given. If a probability distribution is given find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied does the table show a probability distribution
College students are randomly selected in groups of three, the random variable x is the number in the group who say that they take one or more online courses. Determine ether a probability distribution is given. If a probability distribution is given find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied
does the table show a probability distribution
Transcribed Image Text:**Probability Distribution Table**
The table below represents a probability distribution of a discrete random variable \( x \). Each value of \( x \) is associated with a probability \( P(x) \).
| \( x \) | \( P(x) \) |
|---------|------------|
| 0 | 0.104 |
| 1 | 0.356 |
| 2 | 0.397 |
| 3 | 0.143 |
**Explanation:**
- The table consists of two columns: the first column represents the possible outcomes (\( x \)) of a random experiment, and the second column represents the probability (\( P(x) \)) of each outcome occurring.
- For outcome \( x = 0 \), the probability \( P(x) \) is 0.104.
- For outcome \( x = 1 \), the probability \( P(x) \) is 0.356.
- For outcome \( x = 2 \), the probability \( P(x) \) is 0.397.
- For outcome \( x = 3 \), the probability \( P(x) \) is 0.143.
The probabilities \( P(x) \) should sum to 1, reflecting all possible outcomes of the experiment. This table is used to understand the likelihood of each potential outcome.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
Step 1
Random variables are of 2 types, discrete and continuous. A discrete random variable can only take countable number of possible values. A continuous random variable can take infinitely many values.
The probability distribution of a random variable includes all the possible values of the random variable along with the probabilities. The expected value of the random variable is same as the mean.
