Homework Help is Here – Start Your Trial Now!
Math
Probability
Q 1 If X is a random variable with distribution X: 0 1 2 3 111 P(X): - - - - 4444

Q 1 If X is a random variable with distribution X: 0 1 2 3 111 P(X): - - - - 4444

A First Course in Probability (10th Edition)
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
icon
Related questions
Question
100%
Q 1 If X is a random variable with distribution X: 0 1 2 3 P(X): 1111 44 44 Find the mean, Variance and standard deviation. Q 2 If X is a random variable with distribution X: 0 12 3 4 P(X): 0 K 2K 3K 4K Explain the following: (i) For which value of K, P(X) is probability mass function? (ii) Find the following probabilities: (a) P(1 ≤ X < 4). (b) P(2 < X < 4). Q3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (²) and standard deviation (o) of the numbers on the balls. Q4 A special six-sided die is made in which 2 sides have 6 spots, 3 sides have 4 spots, and 1 side has 1 spot. If the die is rolled, find the expected value of the number of spots that will occur. Q5 Let X-B(4,0.6). Find the following (i) P(X = 2) (ii) P(1 < X < 4) (iii) Also find mean and variance. Q6 Let X~P(2). Find the following P(X = 0; 2) P(X = 2; 2) Also find mean and variance. (i) (ii)
Transcribed Image Text:Q 1 If X is a random variable with distribution X: 0 1 2 3 P(X): 1111 44 44 Find the mean, Variance and standard deviation. Q 2 If X is a random variable with distribution X: 0 12 3 4 P(X): 0 K 2K 3K 4K Explain the following: (i) For which value of K, P(X) is probability mass function? (ii) Find the following probabilities: (a) P(1 ≤ X < 4). (b) P(2 < X < 4). Q3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (²) and standard deviation (o) of the numbers on the balls. Q4 A special six-sided die is made in which 2 sides have 6 spots, 3 sides have 4 spots, and 1 side has 1 spot. If the die is rolled, find the expected value of the number of spots that will occur. Q5 Let X-B(4,0.6). Find the following (i) P(X = 2) (ii) P(1 < X < 4) (iii) Also find mean and variance. Q6 Let X~P(2). Find the following P(X = 0; 2) P(X = 2; 2) Also find mean and variance. (i) (ii)
Q7 From the paired data: X 1 23 4 5 Y 10 8 12 12 16 (i) Find the correlation coefficient (r). (ii) Explain the relationship. (iii) (iv) Find the line of regression. Estimate the value of Y when X = 5. Q8 Find the following probabilities or area. (i) P(Z < 1.23) (ii) P(Z > 1.37) (iii) P(1.45 < z < 1.62) (iv) P(Z < -1.42) (v) P(-1.34 < z < 2.15) Q9 From the paired data set (X,Y): (5,9), (4, 7), (3, 5), (2,3), (1, 1) (i) Find the correlation coefficient (r). (ii) Explain the relationship. Find the line of regression. Estimate the value of Y when X = 10. (iv) Q 10 If X is a normal random variable with mean 4 and variance 25, then find the standard normal variate z for the following data: (i) X = 10 (ii) X = 3.
Transcribed Image Text:Q7 From the paired data: X 1 23 4 5 Y 10 8 12 12 16 (i) Find the correlation coefficient (r). (ii) Explain the relationship. (iii) (iv) Find the line of regression. Estimate the value of Y when X = 5. Q8 Find the following probabilities or area. (i) P(Z < 1.23) (ii) P(Z > 1.37) (iii) P(1.45 < z < 1.62) (iv) P(Z < -1.42) (v) P(-1.34 < z < 2.15) Q9 From the paired data set (X,Y): (5,9), (4, 7), (3, 5), (2,3), (1, 1) (i) Find the correlation coefficient (r). (ii) Explain the relationship. Find the line of regression. Estimate the value of Y when X = 10. (iv) Q 10 If X is a normal random variable with mean 4 and variance 25, then find the standard normal variate z for the following data: (i) X = 10 (ii) X = 3.
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS