The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x
Transcribed Image Text:### Probability Distribution Table
The table below displays a probability distribution for a discrete random variable \(x\). The values of \(x\) range from 0 to 4, and the corresponding probabilities \(P(x)\) are listed alongside each value. The probabilities are as follows:
| \(x\) | \(P(x)\) |
|-------|----------|
| 0 | 0.49 |
| 1 | 0.05 |
| 2 | 0.32 |
| 3 | 0.07 |
| 4 | 0.07 |
**Explanation:**
- Each number under the column \(x\) represents a possible outcome of the random variable.
- The corresponding \(P(x)\) value indicates the probability of each outcome occurring.
- A valid probability distribution requires that all probabilities are between 0 and 1 and that the sum of all probabilities equals 1.
This table is a concise way to view all possible outcomes and their probabilities, which can be used for further statistical analysis and calculations.
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 + ...
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