Calculating mean and variance of probability

In summary, the mean number of students who fail in a course with a 30% failure rate and 8 students is 2.4. The correct equation for the variance is (0.3)(0.7)(1-2.4)^2 + (0.3)(0.7)(2-2.4)^2 + ... + (0.3)(0.7)(8-2.4)^2, which is approximately equal to 23.184. The final step would be to take the square root to find the actual variance.
  • #1
bunnyrabid
2
0

Homework Statement



Given a 30% failure rate, what is the mean number of students who fail, and what is the variance? There are 8 students in the course.

Homework Equations



I think these are the correct equations:
Mean = Probability * Number of students
Variance = Sum from i=1 to 8 of pi(xi-Mean)^2

The Attempt at a Solution



So using the Mean formula I got 0.3*8=2.4
Using the variance formula I got
(0.3)(1-2.4)2+(0.3)(2-2.4)2+(0.3)(3-2.4)2+(0.3)(4-2.4)2+(0.3)(5-2.4)2+(0.3)(6-2.4)2+(0.3)(7-2.4)2+(0.3)(8-2.4)2
which is approximately equal to 23.184 (see variance formula here: wolfram alpha, then click approximate form )
Do I then square root to find the actual variance?

Thanks for any help!
 
Physics news on Phys.org
  • #2
the pi in your variance equation are not correct, you need to have a think about the probability distribution
 

FAQ: Calculating mean and variance of probability

What is the formula for calculating the mean of a probability distribution?

The formula for calculating the mean of a probability distribution is:
Mean (μ) = Σx * P(x)
Where Σx represents the sum of all values in the distribution and P(x) represents the probability of each value occurring.

What is the difference between population mean and sample mean?

The population mean is the average of all values in a given population, while the sample mean is the average of a subset of values (i.e. a sample) from the population. The population mean is typically denoted by the Greek letter μ, while the sample mean is denoted by x̄.

How do you calculate the variance of a probability distribution?

The formula for calculating the variance of a probability distribution is:
Variance (σ²) = Σ(x-μ)² * P(x)
Where Σ(x-μ)² represents the sum of squared differences between each value and the mean, and P(x) represents the probability of each value occurring. Alternatively, the variance can also be calculated as the mean of squared deviations from the mean.

What does the variance tell us about a probability distribution?

The variance tells us how spread out the values in a probability distribution are from the mean. A higher variance indicates that the values are more spread out, while a lower variance indicates that the values are closer to the mean. It is a measure of the variability or diversity of a distribution.

How can we use the mean and variance to compare different probability distributions?

The mean and variance can be used to compare different probability distributions by providing insight into the central tendency and variability of each distribution. For example, a distribution with a higher mean and lower variance may have a higher peak and narrower spread compared to a distribution with a lower mean and higher variance. By comparing the mean and variance, we can gain a better understanding of the shape and characteristics of different probability distributions.

Similar threads

Getting the probability distribution of a random variable
Replies
2
Views
203
Probability of Difference in Means for Two Independent Paint Experiments
Replies
8
Views
2K
Variance of binomial distribution
Replies
8
Views
2K
Transforming Correlated Standard Normals with Cholesky Decomposition
Replies
3
Views
1K
Find mean and variance of a random vector
Replies
2
Views
1K
Math: discrete probability distribution
2
Replies
59
Views
5K
Expected profits in Blackjack - tricky probability problem
Replies
7
Views
2K
Statistics: What is the probability of type I error?
Replies
2
Views
2K
Calculating a moment of a distribution
Replies
11
Views
2K
Probability Distribution Problem
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top