Stat418.2 Midterm2 Review GuideMidterm exam 2 will cover most of chapter 3 and chapter 4 in the textbook. Inparticular, the followings are the topics you should know:Chapter 3. Continuous Random Variables1) Know the basic properties of p.d.f. of a continuous type of random variable.2) Know how to calculate c.d.f. from a p.d.f.3) Know how to compute probabilities such as P(X<a), P(X>a), P(a<X<b) fromp.d.f. via integration, and from c.d.f.4) Know the commonly used continuous type distributions, such as e.g., Unif(a,b), Exp(), Erlang(, k), N(,2)In particular, know their p.d.f., c.d.f., mean and variance.5) Know how to compute expectation of a function of X via integration. Inparticular, the mean E(X) and the variance Var(X).6) Know how to compute the probabilities from a Gaussian random variableusing the c.d.f. function of a standard normal random variable.7) Given the p.d.f. of X, know how to derive the p.d.f. and c.d.f. of a derivedrandom variable Y=g(X), including the support of Y.8) Know how to derive the conditional p.d.f. of a continuous type randomvariable X given an event B, i.e., fX|B(x).9) Know how to compute the conditional expected values, including conditionalmean and conditional variance.(Delta functions and mixed random variables are not required)Chapter 4. Pairs of Random Variables1) Know the properties of joint p.m.f and p.d.f. of a pair of random variables.2) Know how to calculate the joint c.d.f. from the joint p.m.f/p.d.f. of a pair ofrandom variables.3) Know how to derive a joint p.m.f/p.d.f. of a pair of random variables in simplecases, such as the example in the practice problem and the independent case.4) Know how to compute the joint probabilities such as P(X>a, Y>b) etc.5) Know how to derive the marginal p.m.f./p.d.f. from the joint p.m.f./p.d.f.6) Know how to derive the p.m.f./p.d.f. of a function of two random variables.For example, W=X+Y, W=max(X,Y), or W=min(X,Y).7) Know how to compute the expected values of g(X,Y) from the jointdistribution of X and Y. In particular, the covariance X,Y=Cov(X,Y) and thecorrelation coefficient XY=Corr(X,Y).8) Know that Cov(X,Y)=E(XY)-E(X)E(Y), and the meaning of X,Y.9) Know that -1<=XY <=1, and the meaning of XY.10)Know how to derive the conditional joint p.m.f/p.d.f. given an event B, i.e., fX,Y|B(x,y).11)Know how to derive the conditional p.m.f./p.d.f. of X given Y=y, or vise versa,i.e., fX|Y(x|y) and fY|X(y|x).12)Know how to compute the conditional expected values by definition. Inparticular, know how to compute conditional mean and conditional variance.13)Know how to compute the expected value via chain expansion, i.e.,EX(X)=EY(EX|Y(X|Y)). 14)Know the conditions for X and Y being independent.(Bivariate Gaussian random variable is not