UCS410 - Probability & Statistics - Statistics Assignment Help

Assignment Task

Q1) There are n people gathered in a room. What is the probability that at least 2 of them will have the same birthday?

- Use an R simulation to estimate this for various n.

- Find the smallest value of n for which the probability of a match is greater than .5.

- Explore how the number of trials in the simulation affects the variability of our estimates.

Q2) A friend has a coin with probability .6 of heads. She proposes the following gambling game. You will toss it 10 times and count the number of heads. The amount you win or lose on k heads is given by (???? 2 -7k)

- Plot the payoff function.

- Make an exact computation using R to decide if this is a good bet.

- Run a simulation and see that it approximates your computation in part.

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