Let X₁ and X₂ be two independent random variables with normal distributions N(1,9) and N(-3,16), respectively. Find the moment generating function of Y= X₁ + X₂. What distribution is associated with this moment generating function?

Q: Question 3 A particular concentration of a chemical found in polluted water has been found to be…

A: Givenp=0.20n=20Let "x" be the number of fishes survivex~Binomial(n=20,p=0.20)P(X=x)=Cxn×px×(1-p)n-x…

Q: Red, 3 Green and 2 Blue Balls. Find the probability that the 1st is a green or a red, followed by a…

A: HERE GIVEN  TOTAL NUMBER OF BALLS =7 No of RED BALLS=2 No of Blue Balls=2 No of Green Balls=3 AND We…

Q: ion. The statements as written may not be sufficient for a clear argument. You may need to change…

A: The reasoning are of 3 types: Deductive Inductive Abductive The premises are the…

Q: Q6:The following distribution received each day during the past (50) days at the office of a…

A:

Q: The average number of field mice per acre in a 6-acre wheat field is estimated to be 11. (a) Find…

A: We have givenλ = 11X ~ Poisson (λ) => X ~ Poisson (11) Formula: P(X = x ) = e-λλx/x!

Q: Two fair coins are tossed 225 times simultaneously and their outcomes were recorde as: Reduce…

A:

Q: You are given the sample mean and the population standard deviation. Use this information to…

A: Given that  n=45 homes, X bar=$114 , sigma=$15.10 We have to find 90% and 95% Confidence interval.

Q: 2- Let the probability density function of the random variable X is - {² (+)* 0 Then My(t) is f(x) =…

A:

Q: Use the given confidence interval to find the margin of error and the sample mean. (4.41,8.05) The…

A: Given,(4.41 , 8.05)Upper limit(UL)=8.05Lower limit(LL)=4.41

Q: 4. Let X denote the mean of a random sample of size n from the distribution N(u, 10) and P(x -…

A: here given ,  p(x¯ - 12 < μ < x¯ + 12) =  0.964  here population  follow normal distribution…

Q: In a certain city district, the need for money to buy drugs is stated as the reason for 71% of all…

A:

Q: Use technology to help you test the claim about the population mean, μ, at the given level of…

A: Givenclaim:μ>1220α=0.08standard deviation(σ)=209.91Mean(x)=1239.17sample size(n)=300

Q: Q3:A: An urn contain three red balls,two blue ball and five white balls, A ball is selected and its…

A:

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters codes can be…

A:

Q: For the statement below, write the claim as a mathematical statement. State the null and alternative…

A: From the provided information, An amusement park claims that the mean daily attendance at the park…

Q: 2. If X and Y are two random variables, having joint density function 1 -(6-x-y) 0≤x≤ 2, 0≤ y ≤ 4 24…

A: According to our guidelines we can solve only first three sub-parts.  For remaining sub-parts please…

Q: * The Fourier Transform of x(t) = [u(t)-u(t-2)][u(t) — u(t − 1)] 8(t – 0.5) cos(2πt) - exp(-j0.5w) O…

A:

Q: A null hypothesis is rejected with a level of significance of 0.05. Is it also rejected with a level…

A: It is given that the null hypothesis is rejected with a level of significance of 0.05.

Q: The random variables X and Y describe the outcome of two independent tosses with a dice Let Z = X +…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts [probability…

Q: Answer d and e

A:

Q: The marks of students in mathematics are normally distributed with a mean of 85 in a university. In…

A: Given data is Mean(μ)=85sample size(n)=36P(x1>88)=0.0013

Q: The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year…

A: The mean is 3.26 and the standard deviation is 0.15.

Q: Your friend grabs a die at random from a drawer containing two 4-sided dice, one 8-sided die, and…

A:

Q: Find the critical value z necessary to form a confidence interval at the level of confidence shown…

A: GivenConfidnece level(c)=0.96

Q: A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed,…

A: From the provided information, The hypotheses are as follow: H0: p = 0.8 Ha: p ≠ 0.8

Q: The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean…

A: It is given that  Mean = 20 minutes  Standard deviation = 5 minutes    Note: The p-value is taken…

Q: The annual salary for one particular occupation is normally distributed, with a mean of about…

A: Given: The sampling distribution of mean is =$126,000 Standard deviation = $18000 sample = 30

Q: A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is at most 2.4…

A:

Q: Use the normal distribution of SAT critical reading scores for which the mean is 514 and the…

A: It is given that  Mean = 514 Standard deviation = 122   Note: The p-value is taken from standard…

Q: 2- Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(A|B) = 0.1. Then P(A|AUB) is O True…

A:

Q: 37% of working mothers do not have enough money to cover their health insurance deductibles. You…

A: Binomial probability pmf has used.

Q: e values of a and B. e probability that on any given day the daily power consumption will exceed 14…

A: Given Mean=12 Variance=48

Q: The monthly utility bills in a city are normally distributed, with mean of $100 and a standard…

A: Given,Mean(μ)=$100standard deviation(σ)=$12

Q: (a) The probability that fewer than 7 field mice are found on a given acre is (Round to four decimal…

A: It is given that the mean is 12.

Q: Here are the shopping times (in minutes) for each of sixteen shoppers at a local grocery store.…

A: Solution-: (a) We complete the group frequency distribution table for the data (b) Construct a…

Q: Determine whether the claim stated below represents the null hypothesis or the alternative…

A: Null hypothesis is denoted by H0.

Q: The population mean and standard deviation are given below. Find the required probability and…

A: Given that   The data is normally distributed. Sample size (n) = 75 Population mean (μ) = 228…

Q: Suppose that P(A/B) = 0.4 and P(B) = 0.5. Determine the following: P(ANB) b. P(A'ΜB) a.

A: Given data is P(A/B)=0.4P(B)=0.5

Q: 2- Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(A|B) = 0.1. Then P(A|AUB) is O True…

A:

Q: The grade point averages (GPA) for 12 randomly selected college students are shown on the right.…

A: From the provided information, Sample size (n) = 12

Q: When flipping a coin, two outcomes are possible, such as head and tail. what is the sample space ?

A: GivenA coin is flipped one time

Q: What is the probability that he/she does not study any of the three languages? (b)  What is the…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPARTS  R = Russian language  E = English Language  G…

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: Find the probability P (0<x< for f(x) = x². cos x³ 3 TU 0.235 O 0.304 O 0.908 O 0.413 O 0.678 O…

A:

Q: Match the alternative hypothesis shown below with s graph to the right. Then state the null…

A: It is given that the alternative hypothesis  Ha: μ ≠ 6. Here, need to find out the correct choice…

Q: responding z-scores. If convenient, use technology to find the z-score. P18 ck to view page 1 of the…

A: Given that.   X~N( μ , ?^2 )   μ=0     , ?=1   Z-score =( x - μ )/?

Q: The probability that the mean height for the sample is greater than 65 inches is (Round to four…

A: It is given that  Mean, μ = 64.2 Sample size, n = 65 Standard deviation, σ = 2.55

Q: Exposure of a certain fruit fly population to an insecticide has produced 2 kinds of mutations. 20%…

A:

Q: Consider the sample space S= {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}, where each point is assumed…

A:

Q: The average individual monthly spending in the United States for paging and messaging services is…

A: Suppose a random variable X has mean µ and standard deviation σ. Therefore, the z-score of that…