A univariate Gaussian or normal distributions can be completely determined by its mean and variance. Gaussian distributions can be applied to a large numbers of problems because of the central limit theorem (CLT). The CLT posits that when a large number of independent and identically distributed ((i. i.d.) random variables are added, the cumulative distribution function (cdf) of their sum is approximated by the cdf of a normal distribution. Recall the probability density function of the univariate Gaussian with mean μ and variance σ2 , N(μ,σ2) : fX(x)=12πσ2−−−−√e−(x−μ)2/(2σ2).

Vinny is interviewing for a job. he wants his take home pay to be at least $42,000.what is the least salary he can earn if he pays 25% income tax?

Data for the height of a model rocket launch in the air over time are shown in the table. darryl predicted that the height of the rocket at 8 seconds would be about 93 meters. did darryl make a good prediction? yes, the data are best modeled by a quadratic function. the value of the function at 8 seconds is about 93 meters. yes, the data are best modeled by a linear function. the first differences are constant, so about 93 meters at 8 seconds is reasonable. no, the data are exponential. a better prediction is 150 meters. no, the data are best modeled by a cubic function. a better prediction is 100 meters.

Which of these phrases uses parallelism to create a sad tone?