Probability, Random Variables, and Probability Distributions
Which function is used to calculate the probability of a geometric random variable Y being equal to a specific value k?
Cumulative distribution function (CDF).
Probability mass function (PMF).
Mean and standard deviation.
Probability density function (PDF).
If it's known that after five patients were treated without reaction to a new medication, there was an approximately 10% chance that this could occur under normal conditions, what's implied about the single-trial reaction rate?
(five successes) ≈ 20%, (one-trial success rate + p)
P(five successes) = (one-trial success rate)^5 = 10%, one-trial success rate ≈ 20%
(five successes) = n(p+q), (one-trial success rate, p, q = probability of failure) ≈ 20%
(five successes) = np, (one-trial success rate, p, n = number of trials) ≈ 20%
If a player free-throw shooter succeeds % but misses several times in a row during a game, would this imply anything about their true shot-making skill level?
Potentially learned opponents' defensive strategies and have adapted
Maybe affected by temporary factors like fatigue or pressure
Yes, implies a decrease in overall ability
No, random variations exist independently of past performance
When rolling a fair six-sided die, what is the expected number of rolls needed until getting a five for this geometric scenario?
36
6
6/5
5
If you toss a fair coin repeatedly, what is the probability that your first head appears on your second toss?
0.125
0.75
0.5
0.25
What is the probability that a test will require more than 10 components to be tested before detecting a defect, given that the probability of a component failure is set at 0.111?
0.6847
0.07383
0.101
0.2645
0.3487
What is the expected value of trials needed for a basketball player with a free throw success rate of to make her first basket?
np = n(1/5), where n is an integer.

How are we doing?
Give us your feedback and let us know how we can improve
When researching consumer behavior patterns, if an analyst estimates that customers make purchases on average once every eight visits to an online store, what is the probability that a purchase will occur on any given visit?
0.124
0.122
0.125
0.127
Which term describes an experiment where there are repeated trials with two possible outcomes and we are interested in finding out when we get our first 'success'?
Normal Model Scenario
Binomial Setting
Central Limit Theorem Example
Geometric Setting
What is the possible range of values for a geometric random variable?
All positive integers.
All non-negative integers.
All real numbers.
All natural numbers.