Given a normal distribution with mu = 100 and sigma = 10, what is the probability that X is greater than 75? Given a normal distribution with mu = 50 and sigma = 4, what is the probability that x is greater than 43? If Y is normal with μ = 200 and σ = 12, what is the pr...
In most cases, the best way to learn anything is to break it down into concepts. This goes for concepts inprobability and statisticstoo. Moment-generating functions (MGF) are one of these concepts all data scientists should know. The following guide will answer what they are and how you can...
What happens if the variance is zero in a probability? x P(X = x) -3 0.17 -1 0.28 1 .015 3 0.27 5 0.13 What is the variance? a. 6.9676 b. 2.6396 c. 4.5727 d. 5.8776 e. 8.0278 Suppose X, Y are joint Gaussian variables with s.d.'s 1 and 3 respectively and covariance -2...
What is cumulative generating function? The cumulant generating function isK(t) = μ(et− 1). All cumulants are equal to the parameter: κ1= κ2= κ3= ... = μ. The binomial distributions, (number of successes in n independent trials with probability p of success on each trial). Th...
The Central Limit Theorem can be proven in many lines by analyzing the moment generating function (mgf) of (sample mean – population mean)/?(population variance / sample size) as a function of the mgf of the underlying population. The approximation part of the theorem is introduced by expand...
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments MGF would like to acknowledge support from the Robert Campeau Family Foundation/Dr. C.H. Tator Chair in Brain an...
while for the mixed "discrete/continuous" mass/density function, it is 00 outside the interval [ai,ki][ai,ki], it has a continuous part that is the density of a uniform U(ai,bi)U(ai,bi),1bi−ai1bi−ai but for ai≤zi<kiai≤zi<ki, and ...
The chi-square distribution is the continuous probability distribution which has positive shaped, and the parameter of the chi-square probability distribution is a degree of freedom, and it is extensively used to test the goodness of fit.
In given case, find the probability of x successes in n Bernoulli trials with success probability p for each trial. x = 2, n = 3, p = 0.65 Round your answers to three decimal places. The probability is [{Blank}]. What is ...
Suppose the researcher considers a random variable (say X) assuming the number of failures before the first success of the independently distributed Bernoulli trials; the probability of success be p, then X is said to have a geometric distribution with parameter p. Answe...