9. For each of the following, determine whether the given values can serve as the values of a distribution function of a random variable with the range x = 1,2,3, and 4: (a) F(1) = 0.3, F(2) = 0.5, F(3) = 0.8, and F(4) = 1.2; (b) F(1) = 0.5, F(2) = 0.4, F(3) = 0.7, and F(4) = 1.0; (c) F(1) F(4) = 1.0. %3D %3D 0.25, F(2) 0.61, F(3) 0.83, and

9. For each of the following, determine whether the given values can serve as the values of a distribution function of a random variable with the range x = 1,2,3, and 4: (a) F(1) = 0.3, F(2) = 0.5, F(3) = 0.8, and F(4) = 1.2; (b) F(1) = 0.5, F(2) = 0.4, F(3) = 0.7, and F(4) = 1.0; (c) F(1) F(4) = 1.0. %3D %3D 0.25, F(2) 0.61, F(3) 0.83, and

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

(CO 3) Consider the following table: Defects in batch 0 1 2 3 4 5 Find the variance of this variable. 1.40 1.49 1.88 1.97 Probability 0.21 0.19 0.30 0.15 0.11 0.04
Let Y₁, Y₂, .. Yn denote a random sample from an exponential distribution with mean 0. a. Show that Ô1 = nY(1) and ĝ2 = Ỹ are unbiased estimators for 0. b. Find the efficiency of ₁ relative to 02. c. Which of these two estimators is superior?
Suppose you have a sample of 9 observations Y1,...,Y, from a normal population with mean 2 and variance 4. Let Y and S denote the sample mean and sample variance, respectively. What is the distribution of E ( (a) (b) 653 (c) Suppose X1,X2, X3, X4, X5 are independent random variables from a normal population with mean 0 and variance 4. Define S3 = E(X, - X). What is the distribution of 253 + S3?
Take a=1 in the question
1. Fit a Gaussian distribution N(x,o?) to the following data. This means that we want to model and represent the given data, in a probabilistic way, using a Gaussian distribution. Then, sketch the distribution. X = [0,0,0.1,0.5,0.9,0.2 ,0.1] Hint: Find the sample mean and sample variance of the data.
2. Let X be a random variable with the following probability distribution: -3 6 F(x) | 1/6 1/2 1/3 Find o?gox for the function g(X) = 3x² + 4.
Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
We have the following information regarding the random variables X, X, and X3: Var(X1) = Var(X2) = Var(X3), Px, X2 = 0.2, pxX, = 0.5, px X Calculate the correlation between X+ X3 and X2 + X3. (i.e. calculate px+Xs.X2+X3) 0.9. %3D