Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

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Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

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Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Students are asked to move an x-axis slider on a normal distribution to make the area to the left of the slider equal to a certain percentage. The 6 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Rolling a pair of dice. Find probability that at least one die shows a given number.

Students are shown a normal distribution, and a slider that moves the distribution horizontally. They are asked to move it so that the mean is equal to a particular value.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Given normal distribution $\operatorname{N}(m,\sigma^2)$ find $P(a \lt X \lt b),\; a \lt m,\;b \gt m$ and also find the value of $X$ corresponding to a given percentile $p$%. 

Given descriptions of  3 random variables, decide whether or not each is from a Poisson or Binomial distribution.

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Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

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Get the student to upload their experimental data in a CSV file, then ask them to compute statistics on it.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.