* Discrete Random Variable = can take countable number of values / Continous = values are uncountable * Probability distribution: a table, a formula, or graph that describes the values of a random variable and the probability associated with these values. * Requirements of Probabilities P(x) = 1 ; Prob must lie between 0 and 1 * Population Mean = E(x) = (x)P(x) Population Variance =( x to the second power)P(x) – Mean squared * Standard Deviation = the square root of variance
* Law of Expected Value: E(c)=C , E(x+c) = E(x) + C, E(cX) = cE(x) * Laws of Expected Value = V(c)=0 , V(x+c) = V(x), V(cX) = c^2V(x) * Bivariate or Joint Probability Distribution: a table, formula, or graph that describes the joint probabilities for all pairs of values of x and y (two random variables) * Binomial Probability Distribution:
* P(X=x) = P(X) = number of trials / (#ofsuccesses)(#offailures) X (Success rate)^#ofsuccesses(Fail rate)^(#offailures) * Mean of BPD = NP (Number of trails)(Success Rate) Variance = NPQ (FailRate) SD = Square Root Variance * At least N = P(x>or equal 16) = 1-P(x < or equal to 15) P(x<14) =P(x< or equal 13) P(x>12) = 1 – P(x< or equal 12) * P(10<orequal X <orequal 21 P(X<orequal21) – P(X<orequal9) * Poisson Probability Distribution = the probability of X events/Successes in a specific interval. Chapter 6
* Conditional Probability = P(A/B) = P(A and B) / P(B) , Two events are related; A given B * P(A) + P(A^c) = 1 (COMPLEMENT)
* Sample Space = All Possible Outcomes
* Categorical or Qualitative Variable = diff. categories are distinguished by some non-numeric characteristics * Numerical or Quantiative = #’s represents counts or measurements (weights, #ofpets, annual income) * Ratio Level/Interval = Observations are numerical (height, weight, prices) * Nominal Level = observations are categories, names,...