**. **

**Binomial Probability Law Probability of exactly ‘r’ successes in ‘n’ independent trials is given by P(r) = n! / r!(n-r)! * pr q(n-r) where p = prob. **

**law** of diminishing returns: The **law** of diminishing returns is an economic principle stating that as investment in a particular area increases, the rate of profit from that investment, after a certain point, cannot continue to increase if other variables remain at a constant. 3 and P (B) =.

**If the P (A or B)=. **

**. **

**The concept of a probability density function of a single random variable can be extended to probability density functions of more than one random variable. **

**A conditional probability , on the other hand, is the probability that an event occurs given that another specific event has already occurred. 9.**

**. **

**The rule. Marginal Distributions Consider a random vector (X,Y). The concept of a probability density function of a single random variable can be extended to probability density functions of more than one random variable. **

**The probability for success equals p. The basic property of E is that of linearity: if X and Y are random variables and if a and b are constants, then E ( aX + bY) = aE ( X. **

**The basic property of E is that of linearity: if X and Y are random variables and if a and b are constants, then E ( aX + bY) = aE ( X. **

**Binomial Probability Law Probability of exactly ‘r’ successes in ‘n’ independent trials is given by P(r) = n! / r!(n-r)! * pr q(n-r) where p = prob. **

**Rule 2: For S the sample space of all possibilities, P (S) = 1. Mar 20, 2016 · Joint, Marginal, and Conditional Probabilities. **

**1, you can see that Bayes' rule gets. , coin ﬂips, packet arrivals, noise voltage • Basic elements of probability: Sample space: The set of all possible “elementary” or “ﬁnest grain”. **

**, coin ﬂips, packet arrivals, noise voltage • Basic elements of**

**probability**: Sample space: The set of all possible “elementary” or “ﬁnest grain”.**A fun fact of marginal probability is that all the marginal probabilities appear in the margins — how cool is that. **

**Each term in Bayes’ theorem has a conventional name: • P(A) is the prior probability or marginal probability of A. **

**0. The joint distribution encodes the marginal. their joint probability distribution at (x,y), the functions given by: g (x) = Σ y. **

**We can also deﬁne their marginal pmfs pX(x) and pY (y). . . The equation itself is not too complex: The equation: Posterior = Prior x (Likelihood over Marginal probability). A joint probability is the probability of event A and event B happening, P(A and B). . **

**The equation itself is not too complex: The equation: Posterior = Prior x (Likelihood over Marginal probability). **

**. The Central Limit. **

**It is the mathematical rule that describes how to update a belief, given some evidence. **

**= Z R f(x,y)dy 3. **

**So this is equal to: fX(x) ⋅ fY(y) Let’s calculate another marginal distribution—this time from the formula. **

**. **

**Hence the P(Female) = 0. **

probabilitydistribution at (x,y), the functions given by: g (x) = Σ y.