Expected Value and Variance of a 1d discrete random variable
Bernoulli Distribution
Bernoulli Distribution
Interactive Bernoulli PMF
Parameter $\mu$0.50
The vertical red line shows the expected value $E[X] = \mu$.
ML estimator for the Bernoulli distribution
Binomial Distribution
Binomial Distribution
Interactive Binomial PMF ($n=12$)
Parameter $\mu$ (p)0.50
The vertical red line shows the expected value $E[X] = n\mu$.
Poisson Distribution
Poisson Distribution
Interactive Poisson PMF
Parameter $\lambda$ (rate)3.0
The vertical red line shows the expected value $E[X] = \lambda$.
The Poisson distribution provides a good approximation of the binomial distribution when $n$ is large and $\mu$ is small. The rate parameter of the approximating Poisson distribution is $\lambda = np$.
ML estimator for the Poisson distribution
Categorical Distribution
Multinomial Distribution
Interactive Mendelian Cross Simulation
Simulate 10 samples of $n=12$ dihybrid crosses.
Probabilities: $9/16$ (Round/Yellow), $3/16$ (Round/Green),$3/16$ (Wrinkled/Yellow), $1/16$ (Wrinkled/Green).