Exercise 1. C Suppose we performed the experiment with replacement: each time sampling a ball we...
Suppose we performed the experiment with replacement: each time sampling a ball we would return it back. What would then be the distribution of X?
1. Generating the sampling distribution of the mean Аа Аа Suppose you use sampling techniques to estimate the mean of the numbers 1, 2, 3, 4, 5, 6, 7, and 8. To do this, you perform an experiment in which you roll an eight-sided die two times (or equivalently, roll two eight-sided dice one time) and calculate the mean of your sample The true mean (u) of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 is and...
Suppose that a person plays a game in which he draws a ball from a box of 10 balls numbered 0 through 9. He then puts the ball back and continue to draw a ball (with replacement) until he draws another number which is equal or higher than the first draw. Let X denote the number drawn in the first draw and Y denote the number of subsequent draws needed. (a) Find the conditional probability distribution of Y given X...
Suppose that a person plays a game in which he draws a ball from a box of 10 balls numbered 0 through 9. He then puts the ball back and continue to draw a ball (with replacement) until he draws another number which is equal or higher than the first draw. Let X denote the number drawn in the first draw and Y denote the number of subsequent draws needed. (a) Find the conditional probability distribution of Y given X...
Suppose that a person plays a game in which he draws a ball from a box of 6 balls numbered 1 through 6. He then puts he ball back and continues to draw a ball (with replacement) until he draws another number which is equal or higher than the first draw. Let X and Y denote the number drawn in the first and last try. respectively. a) Find the probability distribution of X (The first draw) b) Find the probability...
Suppose we have the following experiment: choosing a single ball from a bag which has an equal number of red, green, yellow, and blue balls, and then rolling a 6 sided die. What is the size of our sample space?
Energy of a Tossed Ball In this experiment, we will study energy changes using a Motion Detector. OBJECTIVES: • Measure the change in the kinetic and potential energies as a ball moves in free fall. • See how the total energy of the ball changes during free fall. MATERIALS: Computer Lab Pro Logger Pro Vernier Motion Detector Basketball PRELIMINARY QUESTIONS (PHY2048): For each question, consider the free-fall portion of the motion of a ball tossed straight upward, starting just as...
Exercise. Below we have plotted a discrete "sampling of a vector field: -2 2 4 Let C be a circle of radins 3 centered at the origin drawn in a counterclockwise fashion. What concusions seem to be true? This is a gradieut field This is not a gradient field. This field has positive cur This field bas negative curl. c F.dp X Try again Note that the raclias of the circle is irreverent. Exercise. Below we have plotted a discrete...
Suppose we took samples of employees with 30 employees in each sample. If the average satisfaction level is .614 with a standard deviation of .254. What would be the shape of the sampling distribution if we took these samples over and over again and recorded the means of each sample mean?
2. Consider an urn that contains red and green balls. At time 0 there are k balls with at least one ball of each color. At time n we draw out a ball chosen at random.We return it to the urn and add one more of the color chosen. Let X be the fraction of red balls at time n. Show that Xn is a martingale with respect to the filtration (X0,Xi, ,Xn). At time n there are nk balls,...