Solution
a) True as according to central limit theorm as number of draws increases it will converges to the noraml curve
b) False they converges for the sum of draws
c) False it converges to the hostogram of the numbers in the box
d) False sum converges to normal not product
e) True histogram for the numbers drawn converges for the numbers in the box
Draws are being made at random with replacement from a box. The number of draws is...
One hundred draws are made at random with replacement from the box: [1,1,2,3] The draws come out as follows: 45 1’s, 23 2’s, and 32 3’s. 1. the standard deviation of the sum of the draws is: 2. the standard deviation for the number of 1’s is:
Eight draws are made at random with replacement from the box with numbers: 1,2,3,3,3. Find the probability of drawing exactly two 3's
One hundred draws are made at random with replacement from 1, 2, 3, 4, 5. What is the chance of getting between 8 and 32 tickets marked 5?
Two draws are made at random without replacement from the digits {1,2,3,4}. Let X1 be the first digit drawn and X2 the second. Let M=max(X1,X2) and S=X1+X2. a) Find ?(?). b) Make a joint distribution table for M and S. c) Use the table in Part b to find the distribution of M. d) Find ?(?).
A box contains a large number of red and blue tickets; the proportion of red tickets is known to be 50%. A simple random sample of 100 tickets is drawn from the box. Say whether each of the following statements is true or false, and explain briefly. There is about a 95% chance that the proportion of reds in the sample will be in the range from 40% to 60%. Why is the answer True?
Slaruaru evidol - - 6. (5 pts) Consider a box containing the following numbers. 2, 4, 7, 13, 14 The SD for the box is 4.77. Suppose 25 draws are made at random with replacement from the box. The expected value for this sum is == The standard error for this sum is = HINT: See the discussion on pages 291-292. 7. (5 pts) A die is rolled 48 times. The average of the list 1,2,3,4,5,6 is 3.5 and SD...
Q2] (12 Marks): Eight balls, each marked with different whole number from 2 to 9, are placed in a box. Three of balls are drawn at random (with replacement) from box. i. What is the probability that the ball with the number 5 is drawn? ii. What is the probability that the three numbers on the balls drawn are odd? What is the probability of that the sum of the three numbers on the disc is odd. iv. What is...
gnment 12 (Chapters 13 & 14) due 10/24 Random EV and SE Sum.problem Statistics for Chance Numbers: EV and SE of the sum 49 draws are made at random with replacement from a box containing these 6 tickets: 5, 10, 7, 4, 2, 2 a. What is the smallest possible value the sum of the 49 draws could be? Tries 0/3 Submit Answer b. What is the largest possible value the sum could be? Tries 0/3 Submit Answer c. What...
Use the rbinom() function to create a vector of 1000 random observations from the binomial distribution with n=100 and probability of success is equal to 0.4. Calculate the mean and standard deviation statistics for this vector of random draws using the mean() and sd() commands. How do these numbers compare the mean and standard deviation of the binomial distribution when and ? If they are different, why? Make a histogram of this vector using the hist() command.
5 Random Numbers and Histograms [Applied] Let x = x1 + ... + x20, the sum of 20 independent Uniform(0,1) random variables. In R, create 1,000 simulations of x and plot their histogram. On the histogram, overlay a graph of the normal density function with the same mean as x. Comment on any differences between the histogram and the curve. Hint 1: To plot a histogram in R you can build on the following code: library(ggplot2) df <- data.frame( x...