In an urn there are two white, two black and one red ball. Apart from color, they are otherwise the same. Two balls are drawn without bouncing. The number of white (X) and the number of black (Y) spheres are recorded. question a) Calculate the simultaneous point probability of (X, Y). b) Calculate E (X), E (Y), Var (X) and Var (Y). c) Calculate Cov (X, Y) and ρ (X, Y).

In an urn there are two white, two black and one red ball. Apart from color, they are otherwise the same. Two balls are drawn without bouncing. The number of white (X) and the number of black (Y) spheres are recorded. question a) Calculate the simultaneous point probability of (X, Y). b) Calculate E (X), E (Y), Var (X) and Var (Y). c) Calculate Cov (X, Y) and ρ (X, Y).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) or
a) Given P (X) = 0.4, P (Y) = 0.4 and P (X/Y') = 0.25. i) Find the probability that the event Y does not occur. ii) Draw a contingency table to represent the events above. iii) Find P (XU Y).
Let X1 and X2 be independent random variables for which P(Xi = 1) = 2/5 and P(Xi = 2) = 3/5 . Define U = X1 + X2 and V = X1 x X2. Calculate Cor(U, V )
7) Suppose that X and Y are two independent measurements. We can treat these measurements as random variables, where X has the mean of 1 and standard deviation of 2, and Y has the mean of 2 and the standard deviation of 3. For the transformations below, find the mean, variance, and the standard deviation. a) X+Y b) X-Y c) 2X+Y d) X-2Y+1
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
Given P (X) = 0.4, P (Y) = 0.4 and P (X/Y') = 0.25. i) Find the probability that the event Y does not occur. ii) Draw a contingency table to represent the events above. iii) Find P (X UY).
If X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X, Y) lies between the lines 3X + 4Y = 5 and 3X + 4Y = 10?
Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn
If λ = 6 per hour and μ = 6 per hour in an (M/M/1): (5/FIFO) model, find the probability that there is no customer in the system.
It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 50 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 153, Σx2 = 65, Σy2 = 6201, Σxy = 409, and r ≈ −0.991 (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r =
QUESTION 4 a) Given P (X) = 0.4, P (Y) = 0.4 and P (X/Y') = 0.25. i) Find the probability that the event Y does not occur. ii) Draw a contingency table to represent the events above. iii) Find P (XU Y).