Question

A box contains 8 balls numbered 1, 2, . . . , 8. We randomly remove...

A box contains 8 balls numbered 1, 2, . . . , 8. We randomly remove one ball. Let X and Y be the smallest and greatest numbers in the box after this removal and T = X − Y . Find ET and VarT.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Box 1 contains 4 red balls, 5 green balls and 1 yellow ball. Box 2 contains...
Box 1 contains 4 red balls, 5 green balls and 1 yellow ball. Box 2 contains 3 red balls, 5 green balls and 2 yellow balls. Box 3 contains 2 red balls, 5 green balls and 3 yellow balls. Box 4 contains 1 red ball, 5 green balls and 4 yellow balls. Which of the following variables have a binomial distribution? (I) Randomly select three balls from Box 1 with replacement. X = number of red balls selected (II) Randomly...
A box contains 20 different balls numbered from 1 to 20 (different balls have different numbers)....
A box contains 20 different balls numbered from 1 to 20 (different balls have different numbers). At each step, we select a ball uniformly at random, record the number on it, and put it back in the box. This experiment is repeated 10 times. Find the probability that all the numbers recorded were distinct. (2010)2010 (2010)⋅10!2010 10202010 10102010 None of the above. We select four distinct integers from the set {1,2,…,20}, uniformly at random (all quadruples of distinct integers are...
Box A contains 5 white balls and 7 black balls. Randomly choose one ball. If it...
Box A contains 5 white balls and 7 black balls. Randomly choose one ball. If it is white ball, we randomly draw one more from box A, and if it is black, we choose one ball from box B, in which there are 7 white balls and 8 black balls. a) What is the probability that in the second draw we will choose a white ball? b) The second ball is white, what is the probability that the first one...
1. A box contains 3 white and 2 black balls. The white balls are labelled by...
1. A box contains 3 white and 2 black balls. The white balls are labelled by 1, 2, and 3, and the black balls by 4 and 5. A ball is randomly picked from the box. Let ? be the number shown on the picked ball, and ? = 1 if the picked ball is black; ? = 0 otherwise. Find a. ?(? = 1); b. ?(? = 4, ? = 1); c. ?(??); d. ???(?|? = 4).
A bag contains three balls numbered 1, 2, and 3. Two balls are sampled with replacement....
A bag contains three balls numbered 1, 2, and 3. Two balls are sampled with replacement. Let X1 be the number on the first ball sampled and let X2 be the number on the second ball sampled. Find the probability mass function of the sample mean (X1 + X2)/2.
Box 1 contains 2 red balls and one blue ball. Box 2 contains 3 blue balls...
Box 1 contains 2 red balls and one blue ball. Box 2 contains 3 blue balls and 1 red ball. A coin is tossed. If it falls heads up, box 1 is selected and a ball is drawn. If it falls tails up, box 2 is selected and a ball is drawn. Find the probability of selecting a red ball.
A box contains 6 blue balls and 8 green balls. a) You sample 5 balls from...
A box contains 6 blue balls and 8 green balls. a) You sample 5 balls from this box, with replacement. Let X be the number of blue balls in the sample. What is the name of the distribution of X? specify the parameters. b) Find P(X >= 2) c) You sample 5 balls from this box, without replacement. Let Y be the number of blue balls in the sample. What is the name of the distribution of Y. Specify the...
In the pool, there are 8 white balls numbered 1 to 8 and 4 black balls...
In the pool, there are 8 white balls numbered 1 to 8 and 4 black balls numbered 1 to 4. We draw 3 balls without returning them to the pool. What is the probability that: (a) there is (exactly) 1 black ball among the drawn balls? (b) all drawn balls have even numbers?
A bowl contains four balls numbered 1,2,3,4. If two balls are randomly drawn from the bowl,...
A bowl contains four balls numbered 1,2,3,4. If two balls are randomly drawn from the bowl, without replacment , and the random variable X is the sum of the numbers on the two balls drawn. a) Find the probabiltiy density function. b) Find P(x>3) c) Determine the expected value and the standard deviation.
There are six red balls and three green balls in a box. If we randomly select...
There are six red balls and three green balls in a box. If we randomly select 3 balls from the box with replacement, and let X be number of green balls selected. So, X ~ Binomial [n=3, p=1/3] Use R to find the following probabilities and answers. A) How likely do we observe exactly one green ball? B) Find P[X<=2]. C) Find the second Decile (the 20th percentile). D) Generating 30 random observations from Bin(n,p) distribution, where n=3 & p=1/3....