9. Compute the mean and variance for each of the following distribution, whichever way you find to be the easiest. (a) When X has a Bernoulli distribution with parameter p. (b) When X has a binomial distribution with parameters n and p where ne N and 0 < p < 1. (c) When X has a geometric distribution with parameter p with 0 < p < 1. (d) When X has a Poisson distribution with parameter >> 0.

9. Compute the mean and variance for each of the following distribution, whichever way you find to be the easiest. (a) When X has a Bernoulli distribution with parameter p. (b) When X has a binomial distribution with parameters n and p where ne N and 0 < p < 1. (c) When X has a geometric distribution with parameter p with 0 < p < 1. (d) When X has a Poisson distribution with parameter >> 0.

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

II. Tell whether or not the given distribution is a discrete or not. If it's not, identify what properties it violates a, 1 2 3 4 P(x) 0.10 0.20 0.25 0.40 0.05 b. 4 P(x) 0.05 0.25 0.33 0.28 0.08 C. 2 3 P(x) 0.03 0.22 1.01 0.23 0.02 II. Complete the table by finding the unknown 3 P(x) k 4 k 15 15 5 15 15 1. Find k 3 P(x) d 96. 2d 2 25 25 25 25 2. Find d 5. 2.
5. Need help
Suppose that X follows a binomial distribution with n = 100 and p = 0.1. If F(x) is the cumulative distribution function of the Standard Normal distribution. Then using the Normal approximation, the probability P(X = 16) is obtained by O a. F(2.17) - F(1.83) O b. F(1.83) - F(2.17) O c. F(16.5) + F(15.5) O d. F(17.0) - F(15.0)
12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))
7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
7 If X has Poisson distribution with mean 6. what is P(X-7)? Select one: ut of a. 138 b. None of them C. 0.318 d. 0.681 e. 0.138 as page CS Scanned with CamScanner
3. For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n= 65 and p = 0.7 a. Normal approximation is not suitable. b. Normal approximation is suitable.
3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90
The joint probability distribution of x and y is as follows: У p(x, y) 1 .10 .04 .02 1 .08 .20 .06 .06 .14 .30 Q1. What is the value of the marginal probability P(x = 1)? %D Q2. What is the value of the marginal probability P(y = 1)?
1) 1,2, and 3. Please make sure the answer is correct.
5. Assume that X is a discrete random variable with cumulative distribution function (cdf) F(x) given below. F(X) 0-8 0.b t0.2 -2 2 3 ->