The parameter ? in reliability engineering application of exponential distribution is called failure rate of system. The application uses it as a model of time to failure.

When a process contain a sequence of independent trials which don?t depend on each or?s result, and which have outcome eir a ?success? or a ?failure?, trials are called Bernoulli trials.

The Pascal probability distribution is given by following equation,
\(p(x)=\left(x-1 \atop r-1\right) p^x (1-p)^{x-r}\)
Where x=r, r+1, r+2? and r?1 is an integer.

The Poisson probability distribution which has ?=5, we can determine above stated probability using,
P{x?2} = \(\sum_{x=2}^2 \frac{e^{-4} 4^x}{x!}\) = 0.018316 + 0.73263 + 0.146525 = 0.238104.

Sample variance is always square of sample standard deviation. This clarifies that,
sample standard deviation = \(\sqrt{Sample \,Variance}\).

From property, for any normal distribution which has,
\(y = a_1^2 x_1 + a_2^2 x_2 +?+ a_n^2 x_n\)
We have,
\(?_y = a_1 ?_1 + a_2 ?_2 +?+ a_n ?_n\)

Relative frequencies are defined as frequencies of each bin of histogram, divided by total number of observations (n) in data. They are shown on vertical scale of histogram.

The mean of Pascal distribution is given by following equation,
?=r/p
Where r > 1 and an integer and p is probability of success.

The mean of a gamma distribution = \(\frac{r}{?}\) and standard deviation σ = \(\frac{\sqrt{r}}{?}\); so,
\(\frac{\mu}{\sigma} = \sqrt{r}\).

The mean of a sample data with n number of observations is expressed by,
\( \overline{x} = \sum_{i=1}^n x_i \div n \)