Probability Distributions

Math ⇒ Statistics and Probability

Probability Distributions starts at 10 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Probability Distributions. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 11

A die is rolled once. What is the probability distribution for the outcome?

A fair coin is tossed 4 times. What is the probability of getting exactly 3 heads?

A random variable X has a probability distribution with P(X=0)=0.3, P(X=1)=0.5, and P(X=2)=0.2. What is the variance of X?

A random variable X has the following probability distribution: P(X=1)=0.4, P(X=2)=0.4, P(X=3)=0.2. What is the probability that X is greater than 1?

Define a continuous probability distribution and give one example.

Describe the main difference between discrete and continuous probability distributions.

Explain the difference between a probability mass function (pmf) and a probability density function (pdf).

Explain why the sum of probabilities in a probability distribution must be 1.

If a random variable X has a probability distribution such that P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3, what is the probability that X is less than 3?

If a random variable X has a uniform distribution on the interval [0, 2], what is the value of its probability density function (pdf)?

If the mean of a probability distribution is 5 and the variance is 4, what is the standard deviation?

If X is a discrete random variable with the following probability distribution: P(X=0)=0.2, P(X=1)=0.5, P(X=2)=0.3, what is the expected value of X?

What is the probability of getting exactly 2 heads in 3 tosses of a fair coin?

A bag contains 5 red balls and 7 blue balls. Two balls are drawn at random without replacement. Let X be the number of red balls drawn. Find the probability distribution of X.

A continuous random variable Y has the probability density function f(y) = 3y² for 0 ≤ y ≤ 1. What is the probability that Y is less than 0.5?

A random variable X has the following probability distribution: P(X=1)=0.1, P(X=2)=0.3, P(X=3)=0.4, P(X=4)=0.2. Calculate the expected value and variance of X.

A random variable Z is normally distributed with mean 0 and standard deviation 1. What is the probability that Z is between -1 and 1? (Use the empirical rule.)

Let X be a discrete random variable with probability mass function P(X=x) = kx for x = 1, 2, 3, 4. Find the value of k.

Suppose a random variable X has a binomial distribution with n = 8 and p = 0.25. What is the probability that X equals 2? (Give your answer to 3 decimal places.)

Suppose the lifetime (in years) of a certain type of light bulb is modeled by the exponential distribution with mean 4 years. What is the probability that a randomly chosen bulb lasts more than 6 years? (Give your answer to 3 decimal places.)