(b) (5 points) Using CLT, approximate the probability that P(X = 18).
(c) (5 points) Calculate P(X = 18) exactly and compare to part(b).
(b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate...
8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability that P(X > 20). (b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate P(X = 18) exactly and compare to part(b).
(1) (a) Argue using the Central Limit Theorem that one may approximate X ~ by a normal law when n is large. (b) Under the CLT approximation, find a so that P(X > a)- 10 (1) (a) Argue using the Central Limit Theorem that one may approximate X ~ by a normal law when n is large. (b) Under the CLT approximation, find a so that P(X > a)- 10
I need part b and d, which the answers are not 1.0733 and 0.3394. Thanks. Part II: Binomial Distribution & the Central Limit Theorem a) Imagine sampling 5 values from Bin(15,.2), a binomial distribution with 15 trials and success probability of .2 What should be the expected value (mean) of this sample? You should use the CLT (central limit theorem) and should not need to do any coding to answer this. Answer: 33 Part lI: Binomial Distribution & the Central...
6. In this question, you are going to study the approximation to binomial probabilities using the nor mal distribution. The binomial distribution is discrete while the normal distribution is continuous Therefore, we would expect some issues with approximating the binomial with the normal. (a) (2 points) Suppose X ~ Bin (25,04). Calculate E (N) and Var . (b) (4 points) Use the central lit theorem along with (a) to approximate Pr (X 8). Compare this with your result in #4(a)....
22. A true-false exam has 54 questions. Use the CLT to approximate the probabil- ity of getting a passing score of 35 or more correct answers simply by guessing on each question. 6.7.1 Theorem (Central Limit Theorem). Let X1, X2, ... be an infinite se- quence of iid random variables with mean u and standard deviation o, and let Sn = 21–1 X;. Then lim P(Some < x) = P(x). (6.7) It follows that lim P (as so o) =...
8. Using Minitab to illustrate the Central Limit Theorem (CLT), the CLT tells us about the sampling distribution of the sample mean. With Minitab we can easily "sample" from a population with known properties (4,0 , shape). a. Our population consists of integer values X from 1 through 8, all equally likely P(x) = 1/8; x = 1, 2, 3, 4, 5, 6, 7, 8 o = 2.29 Using methods from the beginning of Chapter 4 in the textbook, find...
Problem 5. (5 pts) Expectation Trick, Strong Law and the CLT (a) (2 pts) Let X be the number of fixed points in a random permutation of n elements. We know that EX = 1. Compute EX? and EX”. Hint : Write X as a sum of indicator random variables. The number of fixed points in a random permutation is also known as the matching problem. (b) (1pt) For the same X as in part (a), give Markov and Chebyshev...
Problem 5. (5 pts) Expectation Trick, Strong Law and the CLT (a) (2 pts) Let X be the number of fixed points in a random permutation of n elements. We know that EX = 1. Compute EX2 and EX3. Hint : Write X as a sum of indicator random variables. The number of fixed points in a random permutation is also known as the matching problem. (b) (1pt) For the same X as in part (a), give Markov and Chebyshev...
Problem 5. (5 pts) Expectation Trick, Strong Law and the CLT (a) (2 pts) Let X be the number of fixed points in a random permutation of n elements. We know that EX = 1. Compute EX? and EX3. Hint : Write X as a sum of indicator random variables. The number of fixed points in a random permutation is also known as the matching problem. (b) (1pt) For the same X as in part (a), give Markov and Chebyshev...
(b) (5 points) Calculate this probability exactly and compare to the bound found in part (a). Is this a helpful bound in this case? 9. (10 points) Recall the random variable X in question 4. Sx = [-6,3] and f(t) = x2/81 for reSx (a) (5 points) Using Chebyshev's Inequality, provide an upperbound to the probability 15X P(X2+ +14 > 3.9375). 2