Probability Distributions
Math ⇒ Statistics and Probability
Probability Distributions starts at 10 and continues till grade 12.
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See sample questions for grade 12
Describe the difference between a probability mass function (pmf) and a probability density function (pdf).
A continuous random variable X is uniformly distributed between 0 and 2. What is the probability that X is less than 1?
A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?
A random variable X has a probability mass function given by P(X=0)=0.4, P(X=1)=0.4, P(X=2)=0.2. What is the variance of X?
A random variable X has a uniform distribution on the interval [a, b]. What is the mean of X?
A random variable X has the following probability distribution: P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3. What is the expected value of X?
If a random variable X follows a binomial distribution with n = 10 and p = 0.3, what is the mean of X?
If a random variable X has a normal distribution with mean 50 and standard deviation 5, what is the z-score for X = 60?
Which of the following distributions is most appropriate for modeling the number of emails received per hour?
(1) Binomial
(2) Poisson
(3) Normal
(4) Uniform
Which of the following distributions is symmetric?
(1) Poisson
(2) Binomial (with p = 0.5)
(3) Exponential
(4) Geometric
Which of the following is a continuous probability distribution?
(1) Binomial
(2) Poisson
(3) Normal
(4) Geometric
Which of the following is a discrete probability distribution?
(1) Normal distribution
(2) Binomial distribution
(3) Exponential distribution
(4) Uniform distribution (continuous)
Fill in the blank: The area under the curve of a probability density function (pdf) over its entire range is _______.
Fill in the blank: The Poisson distribution is characterized by the parameter _______.
Fill in the blank: The probability density function (pdf) is used for _______ random variables.
Fill in the blank: The variance of a binomial distribution with parameters n and p is _______.
True or False: The binomial distribution can be used to model the number of defective items in a batch of products.
True or False: The cumulative distribution function (cdf) of a random variable is always non-decreasing.
True or False: The geometric distribution models the number of trials until the first success.
True or False: The mean of a normal distribution is always equal to its median.
