For each of the statements that follow, determine whether it is true (meaning, always true)or false (meaning, not always true), and provide a very brief explanation (not a completeproof). Here, we assume all random variables are discrete, and that all expectations arewell-defined and finite.(a) Let X and Y be two binomial random variables.i. If X and Y are independent, then X + Y is also a binomial random variable.ii. If X and Y have the same parameters, n and p, then X+Y is a binomial randomvariable.iii. If X and Y have the same parameter p, and are independent, then X + Y is abinomial random variable.(b) Suppose that E[X] = 0. Then, X = 0 (i.e. X(w) = 0 Vw = N).(c) Suppose that E[X²] = 0. Then, P(X = 0) = 1.

We are given few statements about the discrete random variable. We have to determine whether they…

Answered: For each of the statements that follow,…

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...

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You and your friend carpool to school. Your friend has promised that he will come pick you up at your place at 8am, but he is always late(!) The amount of time he is late (in minutes) is a continuous Uniform random variable between 2 and 11 minutes. Which of the following statements is/are true? CHECK ALL THAT APPLY. A. It is less likely that your friend is late for more than 10 minutes than he is late for less than 3 minutes.B. The standard deviation of the amount of time that your friend is late is at about 2.60 minutes.C. The mean amount of time that your friend is late is 6.5 minutes.D. None of the above
Business Calculus 2Section 11.2: Continuous Random Variables
Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed. (a) What are possible y-values? O all positive whole numbers O all integers O all real numbers greater than 1 all whole numbers greater than 1 O all positive real numbers (b) List five different outcomes and their associated y-values. Outcome Value of y RRS LLRLLS 6. LRRS 4 RRRS 4 S. 1 .
prove that if random variables X and Y have same characteristic function, then have same distribution.
Let S = {E1, E2, E3} be the sample space of an experiment and let A = {E1}, B = {E2}, and C = events from S. The probabilities of the sample points are assigned as follows: P(E,) = 0.35, P(E2) = 0.30, and P(E3) = 0.35. Find P(BC). {E2, E3} be Select one: O a. 0.65 O b. 0.70 O c. 0.35 O d. 0.30
Prove the statement
Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.
In a certain factory, machines I, II, and III are all producing springs of the same Q.2. length. Machines I, II, and III produce 3%, 2%, and 5% defective springs, respectively. Of the total production of springs in the factory, Machine I produces 30%, Machine II produces 25%, and Machine III produces 45%. If one spring is selected at random from the total springs produced in a given day, determine the probability that it is defective.
Show that the expectation of the sum of two random variables defined over the same sample space is the sum of the expectations. Hint: Let p1, p2, ··· , pn be the probabilities associated with the n sample points; let x1, x2, ··· , xn, and y1, y2, ··· , yn, be the values of the random variables x and y for the n sample points. Write out E(x), E(y), and E(x + y)
A grocery store employs cashiers, stock clerks, and deli/bakery workers. The distribution of employees with and without dependents is shown here. Dependents Cashiers Stock Clerks Deli/Bakery Workers Yes 8 12 3 No 5 15 2 If an employee is selected at random, find the probability that the employee is a stock clerk or has dependents. A grocery store employs cashiers, stock clerks, and deli/bakery workers. The distribution of employees with and without dependents is shown here. Dependents Cashiers Stock Clerks Deli/Bakery Workers Yes 8 12 3 No 5 15 2 If an employee is selected at random, find the probability that the employee is a stock clerk or has dependents. 0.8444 0.60 0.5111 0.4889
Part 1: Suppose that F and X are events from a common sample space with P(F) # 0 and P(X) # 0. Prove that P(X) = P(X|F)P(F) + P(X|F)P(F). Hint: Explain why P(X|F)P(F) = P(Xn F) is another way of writing the definition of conditional probability, and then use that with the logic from the proof of Theorem 4.1.1. %3D Explain why P(F|X) = P(X|F)P(F)/P(X) is another way of stating Theorem 4.2.1 Bayes Theorem.
Probability. Only question b.

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