IEE 380 UPDATED FINAL EXAM QUESTIONS AND
ANSWERS SURE A+
✔✔addition rule - ✔✔P(A u B) = P(A) + P(B) - P(A n B)
probability of A + probability of B - the intersection of A & B because (A n B) is counted
twice in P(A) + P(B)
✔✔combination - ✔✔a selection of r items from a set of n where order does not matter
nCr
✔✔equally likely outcomes - ✔✔whenever a sample space consists of N popssible
outcomes that are equally likely, the probability of each outcome is 1/N
ex: throw of a fair dye
✔✔event - ✔✔an event is a set of outcomes of an experiment (a subset of the sample
space) to which a probability is assigned
✔✔independence - ✔✔if the events E1 and E2 are independent, then P(E1 n E2) =
P(E1)*P(E2)
the outcome of one event does not effect the outcome of another event
✔✔outcome - ✔✔an outcome is a possible result of an experiment
✔✔probability - ✔✔the sum of the probabilities of the outcomes in the event
✔✔random experiment - ✔✔a procedure that is carried out under controlled conditions,
is executed to discover an unknown result, and results in DIFFERENT outcomes even
when repeated in the same manner every time
✔✔discrete sample space - ✔✔a sample space that consists of a finite or countable
infinite set of outcomes
✔✔discrete random variable - ✔✔a variable with a finite or countably infinite range. its
values are obtained by counting
number of scratches on a surface
number of defective parts among 100 tested
✔✔continuous sample space - ✔✔a sample space that contains an interval of real
numbers
, ✔✔continuous random variable - ✔✔a variable with an interval(either finite or infinite) of
real numbers for its range. its values are obtained by measuring
electrical current and voltage
time
✔✔Probability Mass Function (PMF) - ✔✔a mathematical relation that assigns
probabilities to all possible outcomes for a discrete random variables
✔✔Cumulative Distribution Function (CDF) - ✔✔cdf gives the probability that a random
variable will be less than or equal to specific values
the cdf for a random variable X may be expressed as F(X)=P(X<=x)
given the cdf for a random variable, the probability that an outcome will be less than or
equal to a specific value is represented by the area under the probability distribution to
the left of that value
✔✔Expected Value, Mean - ✔✔E(X) =Σ(all x) x*p(x)
✔✔Variance - ✔✔V(X) = E(X^2) - μ^2
✔✔standard deviation - ✔✔the square root of the variance
✔✔E(X^2) - ✔✔E(X^2) =Σ(all x) x^2*p(x)
✔✔Bernoulli PMF - ✔✔p(x) = p^x * (1-p)^(n-x)
✔✔Bernoulli Trial - ✔✔when a random process or experiment results in one of only two
mutually exclusive outcomes
✔✔Binomial PMF - ✔✔p(x) = (nCx)p^x * (1-p)^(n-x)
✔✔Discrete Uniform PMF - ✔✔p(X) = 1/n
✔✔Poisson PMF - ✔✔p(x) = ((λT)^x * e^(-λT)) / x!
✔✔Continuous Uniform pdf - ✔✔This is the simplest continuous distribution and
analogous to its discrete counterpart. If X has the Continuous Uniform distribution:
pdf of X = f(x) = 1/(b-a) for a<x<b
✔✔cumulative distribution function - ✔✔A function giving the probability that a random
variable is less than or equal to a specified value.
ANSWERS SURE A+
✔✔addition rule - ✔✔P(A u B) = P(A) + P(B) - P(A n B)
probability of A + probability of B - the intersection of A & B because (A n B) is counted
twice in P(A) + P(B)
✔✔combination - ✔✔a selection of r items from a set of n where order does not matter
nCr
✔✔equally likely outcomes - ✔✔whenever a sample space consists of N popssible
outcomes that are equally likely, the probability of each outcome is 1/N
ex: throw of a fair dye
✔✔event - ✔✔an event is a set of outcomes of an experiment (a subset of the sample
space) to which a probability is assigned
✔✔independence - ✔✔if the events E1 and E2 are independent, then P(E1 n E2) =
P(E1)*P(E2)
the outcome of one event does not effect the outcome of another event
✔✔outcome - ✔✔an outcome is a possible result of an experiment
✔✔probability - ✔✔the sum of the probabilities of the outcomes in the event
✔✔random experiment - ✔✔a procedure that is carried out under controlled conditions,
is executed to discover an unknown result, and results in DIFFERENT outcomes even
when repeated in the same manner every time
✔✔discrete sample space - ✔✔a sample space that consists of a finite or countable
infinite set of outcomes
✔✔discrete random variable - ✔✔a variable with a finite or countably infinite range. its
values are obtained by counting
number of scratches on a surface
number of defective parts among 100 tested
✔✔continuous sample space - ✔✔a sample space that contains an interval of real
numbers
, ✔✔continuous random variable - ✔✔a variable with an interval(either finite or infinite) of
real numbers for its range. its values are obtained by measuring
electrical current and voltage
time
✔✔Probability Mass Function (PMF) - ✔✔a mathematical relation that assigns
probabilities to all possible outcomes for a discrete random variables
✔✔Cumulative Distribution Function (CDF) - ✔✔cdf gives the probability that a random
variable will be less than or equal to specific values
the cdf for a random variable X may be expressed as F(X)=P(X<=x)
given the cdf for a random variable, the probability that an outcome will be less than or
equal to a specific value is represented by the area under the probability distribution to
the left of that value
✔✔Expected Value, Mean - ✔✔E(X) =Σ(all x) x*p(x)
✔✔Variance - ✔✔V(X) = E(X^2) - μ^2
✔✔standard deviation - ✔✔the square root of the variance
✔✔E(X^2) - ✔✔E(X^2) =Σ(all x) x^2*p(x)
✔✔Bernoulli PMF - ✔✔p(x) = p^x * (1-p)^(n-x)
✔✔Bernoulli Trial - ✔✔when a random process or experiment results in one of only two
mutually exclusive outcomes
✔✔Binomial PMF - ✔✔p(x) = (nCx)p^x * (1-p)^(n-x)
✔✔Discrete Uniform PMF - ✔✔p(X) = 1/n
✔✔Poisson PMF - ✔✔p(x) = ((λT)^x * e^(-λT)) / x!
✔✔Continuous Uniform pdf - ✔✔This is the simplest continuous distribution and
analogous to its discrete counterpart. If X has the Continuous Uniform distribution:
pdf of X = f(x) = 1/(b-a) for a<x<b
✔✔cumulative distribution function - ✔✔A function giving the probability that a random
variable is less than or equal to a specified value.
