29 Questions
What is the sample space of rolling two dice?
36 points
What is the event E = {H} in a coin flip?
The event that a head appears
What is the event E = {2, 4, 6} in a die roll?
The event that an even number appears
What is the sample space of measuring the lifetime of a car?
All nonnegative real numbers
What does the notation [a, b] represent?
The set of all points x such that a ≤ x ≤ b
What is an event in a probability experiment?
A subset of the sample space
What is the probability that each typist is chosen to do the work?
1/3
What is the expression for E[A] in terms of E[Tx] and probabilities?
E[A] = 1 - p1 - px / (1 + E[Tx])(1 - p1)
In a multinomial trial, what is the sum of the probabilities of each outcome?
1
What is the condition for obtaining E[T(i1,..., ir)] in the nonoverlapping case?
If (i1,..., ir) is nonoverlapping
What is the variance of a Poisson random variable with mean 3?
3
What is the purpose of introducing x in the pattern Px = (i1,..., in, x)?
To obtain the mean occurrence time of the pattern P
What is the conditional probability of Xi given that X2 > 0?
pi/(1 - p0)
What is the relationship between E[Tx] and E[T]?
E[Tx] = E[T] + E[A]
What is the expected value of the number of successes in n trials, given that the success probability is u?
nu
What is the expression for E[T] in terms of px and p1?
E[T] = (1/p1)n - 1 / (1 - p1)
What happens when the pattern i1,..., in includes all distinct data values?
We let x be a data value that is not in the pattern
What is the basis for determining the lowest numbered card that has not yet appeared?
The upturned cards
What is the purpose of turning the cards face up until the lowest numbered card appears?
To represent the first cycle
What is the variable Xi in part (e) of the exercise equal to?
1 if one of the cycles ends with card i, and 0 otherwise
What is the result of taking the first door in the prisoner's cell?
Return to the cell after two days
What is the purpose of finding the variance of the number of cycles?
To understand the distribution of the number of cycles
What is the third door in the prisoner's cell?
A path to freedom
What is the probability of the ith person chosen being in favor?
Np/N
What is Var n Xi?
n * Var(Xi) + 2 * Cov(Xi, Xj)
What is E(N) equal to?
∞
What is P{N i} equal to?
(n - i + 1) / n
What is the probability that the graph is connected?
(n - 1)!n / n!
What is the approximate probability that a Poisson random variable with mean n is less than its mean?
1/2
Test your understanding of probability theory with this quiz on sample spaces, specifically when rolling two dice. Learn to identify the possible outcomes and calculate probabilities.
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