b) c) d) Calculate Var (3X + 2Y+1). Obtain the distribution of W=X+Y. (). Compute E
Q: At a certain gas station, 65% of the customers use regular gas, and all the other customers use…
A:
Q: The A event is defined on a sample space S. Which of the following is always true? O a. A'=A O b.…
A:
Q: If Andrei checks his pulse for 4 minutes, what is his rate if he counts 284 beats?
A: We have given that Total minutes = 4 Total beats count = 284 Rate is given by Rate = Total number of…
Q: 1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3…
A: Solution Marginal pmf of X f(x) =P(X=x)=xΣf(x,y) From joint pmf table P(X=1)=f(1, 1) +f(1, 2)+f(1,…
Q: A random variable X has the probability density function given by: The value of b such that P(X ≤ b)…
A:
Q: A salesman works for a base salary of $450 a month plus 4% commission on all the merchandise he…
A:
Q: The probabilities that the secretary of a construction company, her manager, or both will be sick on…
A: Let A=secretary will be sick B=manager will be sickGiven,P(A)=0.04P(B)=0.07P(A∩B)=0.02
Q: Question 3: Conditional probability, Bayes' theorem In a fruit juice company, machine A (crusher)…
A:
Q: Announcements for 81 upcoming engineering conferences were randomly picked from a stack of IEEE…
A: Confidence interval are used to determine the range where the true value of the parameter lies. It…
Q: Q1: If the event A is independent with itself, then P(A) is
A: Given: An event A is independent to itself. Suppose the probability of the event A is P(A).
Q: The number of customers arriving per hour at a certain automobile service facility is assumed to…
A:
Q: A sleeping bag is on sale for $16.78 and has been discounted 40%. What was the original the sleeping…
A: Let the original price of bag is $x Discount =40% of original price =40% * x =0.40x
Q: a) the probability that the time to detect the next piece of debris is less than 3 minutes. b) the…
A:
Q: 4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2),…
A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…
Q: Find the probability for each of the following situations: 1. You get exactly 1 head when flipping…
A: Dear student according to the guidelines we solve only first question when different statement based…
Q: What is the probability of rolling a total of 9 ?
A: It is given that the sample space of rolling two six-sided dice is S={ (1,1) (1,2) (1,3) (1,4) (1,5)…
Q: Show that the following function is a valid probability mass function of the random variable X. p(x)…
A: Each probability mass function p(x) satisfies following two conditions: p(x)>=0, for all…
Q: 5. Let (S2, A, Pr) be an abstract probability space, and let A, B be events. Prove that Pr(B|A) +…
A:
Q: On a multiple-choice test over English vocabulary, LaTosha got 35 out of 36 correct. What percent of…
A: The number of questions correct is 35.
Q: nas, III past, its goblets. Such goblets are designated as "seconds". Assume defective goblets are…
A: It is given that p = 0.10.
Q: In a refrigerator there are 19 bottles of diet soda, 3 bottles of regular soda, and 6 bottles of…
A: Number of bottles of diet soda = 19Number of bottles of regular soda = 3Number of bottles of water =…
Q: Two baseball teams, A and B, have the same capacity and play a series of four games against each…
A: Given information:- Two baseball teams, A and B, have the same capacity and play a series of four…
Q: 3. Let us consider Y = X₁(X₁+X₂), where X₁ and X₂ are two independent Bernoulli random variables…
A: Given that X1 and X2 are independent Bernoulli random variables with parameter p=1/4. That is,…
Q: f If the events A and B are independent with P(A) = 0.50 and P(B) = 0.40, then the intersection…
A:
Q: What is the probability of the coin showing 5 tails given that at least 4 tails are showing?
A:
Q: The distribution of the scores on a certain exam is N(50,5),which means that the exam scores are…
A: Mean(µ) = 50Standard deviations (σ) = 5X ~ N (µ, σ )= N(50, 5)
Q: For the statement below, write the claim as a mathematical statement. State the null and alternative…
A: Given that Population mean μ =5
Q: able Y is the sum of the life expectancy of t of Y. (Write specifically what distribution it n,…
A: Take x1,x2...,x10 be the life span of parts including gamma.
Q: At Roxbury Community College, 7 out of every 10 students take Introduction to Statistics. If there…
A: Given that, At Roxbury community college 7 out of every 10 students take introduction to statistics.…
Q: The following are the ages (in years) of all eight employees of a small company: 53 32 61 27 39 44…
A:
Q: All books are 25% off of the original price at the bookstore. If a book normally the sale price of…
A: Given data, All books are 25% off of the original price If a book normally costs $20 What is the…
Q: region representing planes x = a1, Find the probability that a point (X, Y, Z) lands in a a hollow…
A:
Q: Researchers at a reputable university and a reputable health organization claim that approximately…
A: Given that,p=74% =0.741-p=1- 0.74 = 0.26n = 85
Q: A local university has 2,654 Hispanic students out of a total student population of 23,956. Do the…
A: Given: Total number of students in a local university is 23,956 Number of Hispanic students is 2,654…
Q: The data set of 18 values is given below 3.2, 4.0, 4.2, 2.1, 4.4, 3.8, 4.2, 3.3, 2.8, 4.3, 3.2, 2.7…
A: A stem-and-leaf is a graphical display of a numerical data set. Each data is divided into two parts:…
Q: Suppose that X is a random variable with the probability density function given by (2(1-x), 0≤x≤1…
A:
Q: A computer salesman averages 1.3 sales per week. Find the probability that in a randomly selected…
A: It is given that the A computer salesman averages 1.3 sales per week. So, if we denote the number of…
Q: Obtain the generating functions using the composition method of the following density functions F(x)…
A: see the attachment please.....
Q: Consider the given discrete probability distribution. Find P(X>3). 1 2 3 4 5 P(x) 0.1 0.2 0.2 0.3…
A:
Q: a) Show that for any three events A, B, and C, the probability that at least one of them occurs is…
A: a)
Q: Kilie is an avid collector of action figures based on superhero movies. She has been tracking the…
A: To determine: The absolute and releative change in the item's value from 2016 to 2022 based on the…
Q: How many positive integer solutions are there of the equation x+y+z=5?
A:
Q: Two six-sided fair dice are rolled. The probability that at least one number is odd and the sum of…
A: Given: The two six-sided fair dice are rolled then we get total of 36 order pairs. The probability…
Q: In the following situation, what sort of probability distribution would most likely be utilized to…
A: It is needed to obtain the required probability distribution.
Q: Let A and B be independent events. Denote by the events Ac and Bc are complements of the events A…
A: Answer: (a):
Q: The owner of a small convenience store is trying to decide whether to discontinue selling magazines.…
A: From the provided information, 5% of the customers buy magazines and thinks that he might be able to…
Q: If you flip a coin 3 times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What…
A: From the provided information, We flip a coin 3 times. Total outcomes = 23 = 8 Outcomes are as…
Q: Suppose a total of 789,654 families live in a particular city and 563,282 of them own homes. A…
A: According to the given information in this question We need to find the proportion
Q: 1. A gaming company claimed that their role-playing games take over 65 hours to complete. A sample…
A: Null hypothesis H0:mu=65 Alternate hypothesis H1:mu>65 Calculating test statistics…
Q: dental insurance go in for regular check-ups. What percent of Americans overall will go in for a…
A: Here define events See the dentist for regular check up = R Person have dental insurance = D
PROBABILITY THEORY
Step by step
Solved in 2 steps with 2 images
- Use the moment generating function to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n.Find the distribution of Y = X1 + · · · + Xn.Use the moment generating function technique to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Exponential(θ), for i =1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.Let Y1 and Y2 be independent random variables that are both uniformly distributed on the interval (0, 1). Find P( Y1 < 2Y2 | Y1 < 3Y2).
- If X and Y have the joint probability distributionf(−1, 0) = 0, f(−1, 1) = 1 4 , f(0, 0) = 16 , f(0, 1) = 0, f(1, 0) = 112 , and f(1, 1) = 12 , show that (a) cov(X, Y) = 0;(b) the two random variables are not independent.Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.Let Q be a continuous random variable with PDFfQ(q)= 6q(1 − q) if 0 ≤ q ≤ 1fQ(q) = 0 otherwiseThis Q represents the probability of success of a Bernoulli random variable X, i.e.,P (X = 1 | Q = q) = q.Find fQ|X (q|x) for x ∈ {0, 1} and all q.
- Find the moment generating function of the continuous random variable X∼U (a, b).Let X1, . . . , Xn be random variables corresponding to n independent bids for an item on sale. Suppose each Xi is uniformly distributed on [100, 200]. If the seller sells to the highest bidder, what is the expected sale price? A)Find the pdf of W = Max (X1, X2, …, Xn). B) Find E(W). Hint: Let W = Max (X1, X2, …, Xn). 1. P[W ≤ c] = P[Max (X1, X2, …, Xn) ≤ c] = P[X1 ≤ c, X2 ≤ c,…, Xn ≤ c] 2. Obtain the pdf of W by differentiating its cdf of W.Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.
- Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.Find the moment-generating function of the contin-uous random variable X whose probability density is given by f(x) =1 for 0 < x < 10 elsewhere and use it to find μ1,μ2, and σ2.(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.