Understanding Probability and Statistics is key to making sense of data, predicting outcomes, and solving problems in various fields. With Moogle Math’s Probability and Statistics Solver, you can explore probability distributions, analyze datasets, and solve statistical problems with precision.
Calculate Probabilities
Example: Find P(X>3)P(X > 3) for X∼N(0,1)X \sim N(0, 1).
Input: probability_distribution(distribution="normal", mean=0, std_dev=1, query="P(X > 3)")
Work with Probability Distributions
Example: Find the mean and variance of a binomial distribution with n=10,p=0.5n = 10, p = 0.5.
Input: distribution_properties(type="binomial", n=10, p=0.5)
Perform Hypothesis Testing
Example: Conduct a two-sample t-test.
Input: hypothesis_test(type="t-test", sample1=[1, 2, 3], sample2=[4, 5, 6])
Analyze Data
Example: Calculate the mean, median, and standard deviation for the dataset [4,8,15,16,23,42][4, 8, 15, 16, 23, 42].
Input: data_analysis(data=[4, 8, 15, 16, 23, 42])
Visualize Data
Example: Create a histogram for [1,2,2,3,3,3,4,4,5][1, 2, 2, 3, 3, 3, 4, 4, 5].
Input: visualize_data(type="histogram", data=[1, 2, 2, 3, 3, 3, 4, 4, 5])
Regression Analysis
Example: Perform linear regression for x=[1,2,3],y=[2,4,6]x = [1, 2, 3], y = [2, 4, 6].
Input: regression_analysis(type="linear", x=[1, 2, 3], y=[2, 4, 6])
To get the best results from Moogle, follow these tips
Example: Find P(X<2)P(X < 2) for X∼Poisson(λ=3)X \sim Poisson(λ=3).
Input: probability_distribution(distribution="poisson", lambda=3, query="P(X < 2)")
Example: Calculate the standard deviation for [12,15,20,25][12, 15, 20, 25].
Input: data_analysis(data=[12, 15, 20, 25])
Example: Test \( H_0: μ_1 = μ_2 \) vs \( H_a: μ_1 \neq μ_2 \).
Input: hypothesis_test(type="t-test", sample1=[10, 20, 30], sample2=[15, 25, 35])
Example: Fit a polynomial regression model to \( x=[1, 2, 3], y=[1, 4, 9] \).
Input:regression_analysis(type="polynomial", x=[1, 2, 3], y=[1, 4, 9])