If n components, functioning independently, are connected in series, and if the $$i^{th}$$​ component has reliability $$R_i(t)$$​, then the reliability of the entire system R(t) is given by

The stratified sampling is usually preferred when the nature of population is

If $$p_i$$​ denote the reliability of the $$i^{th}$$ component; $$i=1,2,\ldots,n$$​ then the reliability of parallel system is given by

A queuing system M/G/1 has

If n components, functioning independently, are connected in series, and if the $$i^{th}$$​ component has reliability $$R_i(t)$$​, then the reliability of the entire system R(t) is given by

If $$X_{p\times1}\sim N_p(\mu,\Sigma)$$​​, then AX follows, where A is a matrix of rank q$$\leq p,$$​​​

For the validity of F-test in the analysis of variance, the following assumption is/are made:

The likelihood ratio test is used for testing [1] null hypothesis against [2] alternative hypothesis. Here

Let $$T_n$$​ be an estimator, based on a sample $$x_1,x_2,\ldots,x_n$$​, of the parameter $$\theta$$​. Then $$T_n$$​ is a consistent estimator of $$\theta:$$​​

For a normal distribution, the area to the right hand side of the point $$x_1$$ is 0.6 and to left hand side of the point $$x_2$$​  is 0.7, then we have

A sequence $$\{X_n\}$$​ is said to be a Markov Chain if for all $$i_0,i_1,i_2,\ldots,i_{n+1}\in I$$​ and $$\forall$$​ n