P5. In an experiment, 3 balls are selected with replacement from an urn that contains 4 green balls and 5red balls. Let Xand Y denote the random variables that measure thenumber ofred balls and thenumber ofgreen balls selected respectively.Find: (a) thejointprobability distribution of XandY and (b) P[(X,Y) E A]where A is the region {(x, y) : (x + y) < 3}.

Answered: P5. In an experiment, 3 balls are…

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

11. Suppose X and Y are independent continuous random variables uniformly dis- tributed on the intervals 0
8. Be X a discrete random variable with distribution given by: Select one: a. 1/8 b. 1/4 c. 3/8 d. 5/8
2. a) Let X and Y be independent identically distributed binomial random variables, X~ Bin(3, 0.4) and Y ~ Bin(3, 0.4). i) Compute the probability P(X = 0). ii) Compute the probability that the product XY equals 0, that is, compute P(XY = 0). b) The actual amount of jam (in g) that a filling machine puts into "150 g" jars may be looked upon as a random variable having a normal distribu- tion with σ = 6 and mean μ = 155. What proportion of jars, in the long-run, contain less than 150 g? N(0, 1), Give your answer in terms of the function, where for Z (z) = P(Z), and a give a sketch of the normal curve with a shaded area that corresponds to the required probability.
5. Suppose Y₁, Y2,..., Y are independent random variables whose density is for y0 for some > 0. (a) Show that the MLE for is f(y) = 30y²e-04³ n ÔMLE = ΣΤ (b) Use the R code to estimate the bias and the variance when n = 20 and 0 = 2.
4. Let X₁ N (0,3²), X₂ N(4,4²), and X3 ~ N(-1,22) be independent random variables. Find P (X₁ + X₂ +3X3 <-8), using the table for standard normal distribution.
Suppose that X is a discrete random variable with the follo wing probability mass fundion: 2 3 p(x) | 20/3 | 0/3 2 (1 - €) (3 T(1-8)/3 where OLeLI is a parameter. the following R independent observations were taken from such distribution: (3,0, 2,1,0,3,0,2,I, 0, 2, 1). Use the method of maximum likelihood to find the estimate of o.
Roll two dice and observe the numbers coming up. Define two events by: A="the sum is six," and B-"the numbers are not equal." Find and compare P(B) and P(BIA).
2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.
2. Consider the two discrete random variables X and Y with joint distribution given below: a 1 2 P(Y=b) -1 1/6 1/6 1/6 1/2 1 1/2 1/2 P(X=a) 1/6 2/3 1/6 1 a) Determine E [X Y]. b) Note that X and Y are dependent. Show that X and Y are uncorrelated. c) Determine Var(X + Y). d) Determine Var(X – Y).
Page 264, 4.4.12
M1
6. Choose 2 points (X, Y) uniformly at random from the circle. Find the expected area of the rectangle with opposite corners given by X and by Y.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS