G Let X1,··· ,Xn be iid from the Beta distribution Beta(α = 2,β = 2), which has pdf f (x) = 6 · x · (1 − x) for x ∈ [0, 1] and f (x) = 0 outside [0, 1]. Let F(x) be the cdf of Beta(α = 2,β = 2), and let. Fn(x) be the empirical cdf (EDF) based on the sample X1,··· ,Xn. (a) Find (by intergating the density) the cdf F (x). (b) Plot the curve F (x) using R over the range [0, 1]. (c) For a given x = 0.4, and n = 100, what is the mean (expectation) of the

Part a: select all of the ordered pairs that are located on the graph of the equation. part b: does the graph of the equation represent a function? select all correct answers for part a and one answer for part b.

Suppose that sahil knows that 45 people with ages of 18 to 29 voted. without using a calculator, he quickly says then 135 people with ages of 30to 49 voted. is he correct? how might sohil have come up with his answer so quickly?

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?