QTM 100-EXAM 2 QUESTIONS AND ANSWERS

QTM 100-EXAM 2 QUESTIONS AND ANSWERS

Random variable - Answers - the outcome of a process (X= number of heads in two
flips)
-can be explained by probability distributions

Discrete random variable - Answers - takes on small number of values; table or bar plot

Continuous random variable - Answers - takes on many values; curves or equations

Expected value - Answers - weighted average of the possible outcomes

Linear combination - Answers - ax + by
-E(ax+by)=a×E(X)+b×E(Y)

-V(ax+by)=a2×V(X)+b2×V(Y) (independent)

Normal distribution - Answers - continuous random variable that has bell-shaped and
symmetric distribution (X~ N(mean, std))

Μ - Answers - mean

Σ - Answers - standard deviation

Standard normal distribution - Answers - normal distribution with a mean of 0 and a
standard deviation of 1 -Z~ N(0,1)

Z-score - Answers - standardized random variable

Z=x−μ/ σ∼ N(0,1)

Binomial distribution - Answers - probability distribution for binary categorical variables
-"success" and "failure" or 1 and 0

Binomial random variable X - Answers - number of successes out of the n trials where
the probability of success is p
- X~ Bin (n,p)
-trials are independent and fixed, each trial has two possible outcomes and same prob.
Of success p

Percentile - Answers - the percentage of observations that fall below a given data point

Mean for binomial distribution - Answers - μ = np

Standard deviation for binomial distribution - Answers - σ = √np(1-p)