Chapter 5: Discrete Probability Distributions

Question 1

random variable

Answer 1

• a variable whose numeric value is determined by the outcome of a probability experiment
• usually denoted by capital letter (X, Y, Z)

Question 2

probability distribution

Answer 2

a table or formula that gives the probabilities for every value of the random variable X, where all of the probabilities are between 0 and 1, inclusive

0 ≤ P(X=x) ≤ 1

and the sum of all the probabilities is 1

∑ P(X = x_i) = 1

Question 3

discrete random variable

Answer 3

may have either finitely many possible values or infinitely many possible values that are determined by a counting process

Question 4

discrete probability distribution

Answer 4

• probability distribution for a discrete random variable
• rounding rule for variance and standard deviation: round to one more decimal place than the largest number of decimal places given in the values of the random variable except when the type of data lends itself to a more natural rounding scheme (e.g. currency). When calculating the standard deviation, do not round the value of the variance before taking the square root.

Question 5

expected value

Answer 5

• the value that we expect the random variable to have on average
• the mean of the probability distribution: E(X) = μ
• rounding rule: round to one more decimal place than given in the data or to the natural rounding scheme (e.g. two decimal places for currency)

Question 6

bionomial distribution

Answer 6

• discrete probability function for problems with a fixed number of independent trials, where each trial has only two possible outcomes and one of these outcomes is counted
• round to four decimal places
• binompdf (n,p,x) for X = x
• binomcdf (n,p,x) for X ≤ x
  
  • reduce x by 1 in formula to get X < x
• 1 - binomcdf (n,p,x) for X > x
  
  • reduce x by 1 in formula to get X ≥ x

Question 7

properties of a binomial distribution

Answer 7