Let \(X \sim \text{Uniform(1, 26)}\).

Use a computer to “roll” this 26 sided die \(N = 10\) times and store the results into a numpy array. Use the function

`np.random.choice()`

.Estimate the population mean using only the sample you just created.

Look at your friend’s answer to 2. Did you two get the exact same number? Why not?

Repeat 1. - 3. with \(N = 100\) and \(N = 1000\). Did you and your friend get the same answers? Are these estimates more or less reliable than your solution to 1. with \(N = 10\)?

Create a variable named

`seed`

that stores any integer value you and your friend choose between 1 and 10000.Use the function

`np.random.seed()`

to set the seed to the value`seed`

.Repeat 1. - 3. Explain why this time you and your friend got the same answer.

What is the true population probability \(P(X = 14)\)?

Provide a calculation of \(P(X = 14)\) using the probability density function for a discrete uniform random variable.

Make a line plot with the roll number on the x-axis and the estimated probability of \(P(X = 14)\) on the y-axis. Use the function

`bp.line()`

.

Let \(X \sim \text{Bernoulli}(p = .314)\). Recall, the probability \(p\) is always associated with the value \(1\).

For \(N = 10, 100, 1000\), flip this unfair coin using the function

`np.random.choice()`

. Hint: look up the function documentation to figure out how to assign unequal probabilities.Estimate \(P(X = 1)\) for each sample size \(N\).

Make a line plot with the flip number on the x-axis and the estimated probability of \(P(X = 1)\) on the y-axis. Use the function

`bp.line()`

.