A typical example of a random variable is the outcome of a coin toss. Consider a probability distribution in which the outcomes of a random event aren’t equally likely to happen. Y could be 0, 1, or 2 if the r
Discrete Distribution – This can be applied only when the random variables can be in some limited numbers where the values can be counted. Each possible value is associated with a probability. Discreteprobability distribution functioncan be a poisson distribution, in which shows the occurrence of e...
In the Wald test, the null hypothesis is rejected if where is a pre-determinedcritical value. Thesize of the testcan be approximated by its asymptotic value where is thedistribution functionof a Chi-square random variable with degrees of freedom. The critical value is chosen so as to achieve...
Presents an example from probability and statistics that ties together several topics including the mean and variance of a discrete random variable, the binomial distribution and its particular mean and variance, the sum of ind...
Construction of Example DataAs a first step, we need to create some data that we can use in the examples below:set.seed(946322) # Set random seed x1 <- rnorm(100) # Create normally distributed vector x2 <- runif(100) # Create uniformly distributed vector...
probability distribution for the full range of values for a discrete variable. A discrete random variable can take on a finite or countably infinite number of possible values, such as the number of heads in a series of coin flips or the number of customers who visit a store on a given ...
distribution of real GDP varies significantly as a function of time. Plot the empirical probabilitydensity function (PDF) of real GDP 5 years (20 quarters) into the future. Get YY = permute(squeezeYY(20:,:)),[2 1]); figure histogram(YY(:,1) - YY(:,2),"Normalization","pdf"...
This example shows a reinforcement learning (RL) approach to maximize the probability of obtaining an investor's wealth goal at the end of the investment horizon. This problem is known in the literature as goal-based wealth management (GBWM). In GBWM, risk is not necessarily measured usi...
What is the random probability of a choice from three choices? What does a probability distribution represent? Which of the following numbers could be the probability of an event? 0.34, 1.43, 0.01, 1, 0, -0.44 The probability of an event is 2/7. What are the odds of the same event?
The basic idea of the sequential permutation test is that it can become clear early on which hypothesis is likely to be accepted in the end. The tests have been designed to control the type-I error probability at a nominal level while preserving or controlling a high power, in terms of a...