Problem 6. Tossing a triple of coins 8 points possible (graded) We have a red coin, for which P(Heads) = 0.4, a green coin, for which P(Heads) = 0.5, and a yellow coin, for which P(Heads) = 0.6. The flips of the same or of different coins are independent. For each of the following situations, determine whether the random variable N can be approximated by a normal. If yes, enter the mean and variance of N. If not, enter 0 in both of the corresponding answer boxes. 1. Let N be the number of Heads in 300 tosses of the red coin. mean: Variance: 2. Let N be the number of Heads in 300 tosses. At each toss, one of the three coins is selected at random (either choice is equally likely), and independently from everything else. mean: variance:
Added by Christopher G.
Close
Step 1
Let N be the number of Heads in 300 tosses of the red coin. Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 59 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
3. Let's say that we toss 3 fair coins all independently of each other. It turns out that the first coin comes up as Heads. Let us define Y as the number of Heads in tossing the three coins (including the first one). (a) (3 pts) What is the conditional distribution of the number of heads for the remaining two tosses, which is denoted by X, given that the first coin comes up as Heads? (b) (3 pts) Note that Y = X + 1. What are the expected value and variance of Y?
Sri K.
Cheng Z.
Problem 5 6.0 points possible (graded, results hidden) The probability of Heads of a coin is y, and this bias y is itself the realization of a random variable Y which is uniformly distributed on the interval [0, 1]. To estimate the bias of this coin, we flip it 6 times, and define the (observed) random variable N as the number of Heads in this experiment. Throughout this problem, you may find the following formula useful: For every positive integers n, k, ∫[0 to 1] x^n(1 - x)^k dx = n!k! / (n + k + 1)! 1. Given the observation N = 3, calculate the posterior distribution of the bias Y . That is, find the conditional distribution of Y , given N = 3. For 0 ≤ y ≤ 1, f_Y|N (y | N = 3) = 2. What is the LMS estimate of Y , given N = 3? (Enter an exact expression or a decimal accurate to at least 2 decimal places.) Ŷ_LMS = 3. What is the resulting conditional mean squared error of the LMS estimator, given N = 3? (Enter an exact expression or a decimal accurate to at least 2 decimal places.)
Jacob F.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD