A company is analyzing the number of times a ticket vending machine fails. Thenumber of failures (X) has a probability mass function given by0.7(0.3)" if x is a non-negative integerf(x) =otherwisea) Determine the probability-generating function of Xb) Using the probability generating function, calculate the mean and variance of thenumber of times the machine fails

Probability Generating Function (p.g.f.): Let X be a discrete random variable with probability mass…

Answered: A company is analyzing the number of…

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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Please do these 3 Qs in excel or show steps, thank you.
Let X be the number of years before a particular type of machines will need replacement. Assume that X has the probability function f(1) = 0.1, f(2) = 0.2, f(3) = 0.2, f(4) = 0.2, f(5) = 0.3. Find the probability that the machine needs no replacement during the first 3 years.
Assume that 1 out of every 5 adults in a local community is unemployed. Approximatethe probability that in a random sample of 100 adults from the community, more than 25are unemployed. Express your final answer in terms of the standard normal cumulativedistribution function Φ.
A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X be the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y be the proportion of time that the walk-up window is in use. The joint PDF is ... fxy (x, y) = 5 (x + y²) • What is the probability that neither window is busy more than one-quarter of the time? • What is f(X)? • What is fy(y)?
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Suppose a fair coin is tossed 3 times. Define the r.v.'s X = number of Heads and Y = 1(0) if H (T) occurs on the first toss. Find the joint probability function for (X, Y).
3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)
Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).
I need part d) ONLY
Three balls are selected at random from a bag containing 2 blue, 3 green, and 4 red balls. Let's define the following random variables B(s) = the number of blue balls drawn G(s) = the number of green balls drawn. Fill the following tables. a) Joint probability mass function pe,(b,g8) and marginal probability mass functions Fa(b) and Fols). Po,o(b,g) B=0 G=0 Pe(b) Po(g). b) Joint probability distribution function FB,6(b,g) and marginal probability distribution functions Fe(b) and Folg). FB,6(b,g) GSO Fo(b) BSO Falg)
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: (c) E(X)= i Round your answer to two decimal places (e.g. 98.76).
X is a random variable with the probability distribution f(X)= ;X= 0,1,2. Then the mean of X is equal to:

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