Probability Distributions Quiz

True (A)

0.4783

<p>1.2</p> Signup and view all the answers

<p>Mean = The average of a probability distribution Variance = A measure of the dispersion of a probability distribution Hyper-geometric Distribution = Models scenarios without replacement Geometric Distribution = Models scenarios with independent trials</p> Signup and view all the answers

<p>Geometric random variable (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>0.0031</p> Signup and view all the answers

<p>1/p</p> Signup and view all the answers

<p>Geometric Distribution = The probability of the first success on trial k Hypergeometric Distribution = Sampling without replacement from a finite population Mean = The average of a probability distribution Variance = A measure of the dispersion of a probability distribution</p> Signup and view all the answers

<p>0.9171 (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>50</p> Signup and view all the answers

<p>The number of trials until the first success (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>A geometric random variable is the number of trials required to get the first success in a Bernoulli process.</p> Signup and view all the answers

<p>p</p> Signup and view all the answers

<p>1/8 (D)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>P(X ≤ x) = P(X = 1) + P(X = 2) + ... + P(X = x)</p> Signup and view all the answers

<p>Tossing a coin, getting a head on the first toss = P = p First success occurs on the third trial after two failures = P = (1-p)²p At least one head in three tosses = 1 - P(X = 0) Rolling a die and getting a six = P = p</p> Signup and view all the answers

The probability of getting the first success on the xth trial in a sequence of independent Bernoulli trials.

A discrete random variable representing the number of trials needed to get the first success in a sequence of independent Bernoulli trials.

The average number of trials needed to achieve the first success in a sequence of independent Bernoulli trials; calculated as 1/p where p is the probability of success.

The average squared deviation of the number of trials from the mean, calculated as (1-p)/p^2 where p is the probability of success.

A probability distribution that describes probabilities of success in drawing a sample in a population without replacement.

A probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.

Each drawn item is put back into the pool of potential items before the next draw. This process ensures that the probability of drawing any particular item remains unchanged in each draw.

Each drawn item is not returned to the pool of potential items. This changes the probability of selecting subsequent items.

The probability of getting a specific number of successes (e.g., men, defective items) in a sample without replacement from a finite population.

The expected value of a hypergeometric variable. It's calculated as n * (N1/N); where 'n' is the sample size, 'N1' is the number of successes in the whole population, and 'N' is the total population size.

The spread of the hypergeometric variable. It's calculated as [(n * (N1/N)) * ((N - n) / (N -1)) * ((N - N1) / N)], where 'n' is sample size, 'N1' is number of successes, 'N' is the whole population size.

Choosing items from a group, where once chosen, the item is not returned to the group.

The number of items that are chosen.

The probability mass function of a geometric random variable X is P(X=x) = (1-p)^(x-1)*p, where p is the probability of success on a single trial and x is the number of trials needed to get the first success.

A fair coin is tossed until a head appears. The probability of getting a head on the first trial is 1/2. The probability of getting a head on the second trial is (1/2)(1/2) = 1/4. The probability of getting a head on the third trial is (1/2)(1/2)(1/2) = 1/8. The probability function in this case is P(X = x) = (1/2)^(x-1)(1/2) = (1/2)^x.

'At most' means including the specific number of trials and all the trials before it. So, the probability of getting the first success in at most 3 trials would be the probability of getting the first success on the 1st, 2nd, or 3rd trial.

'At least' means including the specific number of trials and all the trials after it. So, the probability of getting the first success in at least 3 trials would be the probability of getting the first success on the 3rd trial, on the 4th trial, on the 5th trial and so on.