Start your trial now! First week only $4.99!*arrow_forward*

Question

If X ∼ N (μ_{X} , σ^{2}_{X} ) and Y ∼ N (μ_{Y }, σ^{2}_{Y} ) are independent, then prove

X + Y ∼ N (μ_{X} + μ_{Y} , σ^{2}_{X} + σ^{2}_{Y} )

Tagged in

Math

Probability

Find answers to questions asked by students like you.

Q: When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan. Ra...

A: Number of test batteries are 35. Number of batteries which meet specifically can make the shipment u...

Q: The scores on a standardized test are normally distributed with a mean of 115 and standard deviation...

A: The scores on a standardized test are normally distributed with Mean = 115 Standard deviation = 20

Q: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: A mobile phone shop has 7 colors of iPad, 8 colors of HCT mobile phones and four colors of headphone...

A: Click to see the answer

Q: Stem (ones) Leaf (tenths) 2,6,7,7,7,8,9,9,9 0,2,4,4,7,7,7,8,8,8,9,9,9,9 4 0,0,1,1,2,3,4,4,4,5,6,6,7,...

A: From the stem and leaf plot, we see that the lowest value= 3.2 and the highest value = 6.6

Q: If a confidence interval for the mean is (31≤μ≤87)a) What is the point estimate? b) What is the ma...

A: Click to see the answer

Q: Please solve all parts. it would be a great help. Thank u

A: Let X be the sales made in a day. a)EX=kλ=5×0.9=4.5

Q: According to a research institution, the average hotel price in a certain year was $97.27. Assume ...

A: Click to see the answer

Q: ou measure the length of copperheads in cm. You want to know if there is a difference in length betw...

A: Define the hypotheses: Null hypothesis (H0): H0 : There is no significant difference in the lengths ...

Q: The probability of A is 0.30, the probability of B is 0.40 and the probability of both is 0.30. What...

A: Given: P(A)=0.30 P(B)=0.40 P(A∩B)=0.30 The objective is to find the conditional probability of A giv...

Q: The probability distribution of the random variable X is given in the following table. Find P(1 < X<...

A: P(1<X<4)=?

Q: Given the following probability distribution, what is the expected value? Outcome P(Outcome) 11...

A: Outcome (xi) P(Outcome) (pi) 11 0.11 4 0.15 5 0.14 14 0.13 3 0.47

Q: The tread life of a particular brand of tire is a random variable best described by a normal distrib...

A: Click to see the answer

Q: Data from the Bureau of Labor Statistics indicates that in a certain month, 38.4% of the labor force...

A: Percentage of labor force had high school diploma and few year of education is 38.4%. Percentage of ...

Q: The median is closest to:

A: The discount rate set by bank for past 6 quarters are: Quarter Discount Rate 1 10.0% ...

Q: The fotlowing sample data represents the age of 30 lottery winners. 24 26 27 32 39 40 43 44 46 47 49...

A: the lowest value = 24 and the highest value = 84 so the range= R= 84 - 24= 60 So using the formula ...

Q: A pair of dice is rolled 3 times. What is the probability that a sum of 7 on the 2 dice will occur a...

A: Click to see the answer

Q: The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a stand...

A: The z-score corresponding to 71 inch tall American women is, Thus, the percentage of women that ar...

Q: Let Z be a standard normal random variable and calculate the following probabilities, drawing pictur...

A: we are suppose to answer three sub parts .

Q: The red blood cell counts (in millions of cells per microliter) for a population of adult males ca...

A: Click to see the answer

Q: a game of chance played historically by Canadian Indians involved throwing eight flat beans into the...

A: There are 8 flat and symmetrical beans with 2 sides - one black and the other white. Bean thrower st...

Q: A binomial probability experiment is conducted with the given parameters. Use technology to find the...

A: Let the random variable X follows binomial distribution with parameters (n = 6, p = 0.4) The proba...

Q: Aresearcher studying public opinion of proposed Social Security changes obtains a simple random samp...

A: Given information- We have given that a researcher studying public opinion proposed Social Security ...

Q: For this problem, assume that the committee contains 9 men and 7 women and that three are selected a...

A: Given: Number of men = 9 Number of women = 7 Number of people selected = 3

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule to approximate the given ...

A: According to Bartleby Guidelines, only one question can be solved at a time, kindly post (b) the Mid...

Q: 1. Suppose that E and F are independent events such that Pr[E] = .3 and Pr[F] = .4. (f) Calculate Pr...

A: P(E) = 0.3 P(F) = 0.4

Q: Given P(A) = 0.34, P(B) = 0.60, and P(A or B) = 0.24, are events A and B mutually exclusive?

A: Two events A and B are said to be mutually exclusive if P(A and B)=0 Given P(A) = 0.34, P(B) = 0.60,...

Q: You measure 49 watermelons' weights, and find they have a mean weight of 41 ounces. Assume the popul...

A: The 99% confidence interval for the true population mean watermelon weight is obtained below: The va...

Q: Assume that the random variable X is normally distributed, with mean r=80 and standard deviation a=...

A: Click to see the answer

Q: Haroldo, Xerxes, Regina, Shaindel, Murray, and Georgia are invited to a dinner party. They arrive i...

A: Given data: The total number of guests invited to the party is n=6. The expression for the proba...

Q: The scores on a standardized test are normally distributed with a mean of 90 and standard deviation ...

A: Since z-score is the measure of how far is the standard deviations from the mean. Z-score would be n...

Q: 1. Suppose that E and F are independent events such that Pr[E] = .3 and Pr[F] = .4.(a) Find Pr[E ∩ F...

A: This is a fact of probability related to independent events . This is very useful in statistics .

Q: DPMO is a commonly used lean six sigma metric. Suppose there are 6 defect opportunities (critical ch...

A: Find DPMO for the given problem: It is given that, there are 6 defect opportunities per order. The s...

Q: For events A and B, using the axioms of probability, prove that P(AB) ≤ P(A).

A: For events A and B, using set theory, A=A∩B+Bc∩APA=PA∩B+PBc∩APA=PAB+PBcAPA=PAB+PBcAPAB=PA-PBcA⋯⋯1 Ac...

Q: Scott wants to find a 95% confidence interval for the average GPA for Allegany College of Maryland s...

A: Click to see the answer

Q: A poker hand consists of five cards from a deck of 52. Order does not matter. In how many ways can...

A: A poker hand consists of five cards from a deck of 52. Order does not matter i.e. combination is u...

Q: 4.5-4 a and b only

A: Solution 4.5.4 Given information Let X and Y have bivariate normal distribution with parameters μX=7...

Q: In the country of United States of Heightlandia, the height measurements of ten-year-old children ar...

A: Click to see the answer

Q: A single, six-sided die is rolled. Find the probability of rolling an even number or a number less ...

A: Click to see the answer

Q: Solve full problem

A: Hi! Thank you for the question As per the honour code, We’ll answer the first question since the exa...

Q: 4.5-7 a and b only

A: Click to see the answer

Q: In 2017, the SAT was scored out of 1600. The average SAT scores among the 925 Texas students who sta...

A: Given Information: First sample Sample size (n) = 925 Mean (x¯) = 1148 Second sample: Sample size (m...

Q: Given P(E) = 0.91, what is P(E')?

A: Use compliment rule,

Q: Consider a random 3 digit number from 000 to 999 (1000 in total). What is the probability of getting...

A: Given that there are total 1000 numbers. We have to find the probability of getting a number with...

Q: We wish to conduct a study on the proportion of students who are smokers at UCT. it is estimated tha...

A: Click to see the answer

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit...

A: If = average distance in feet for 49 fly balls, then give the distribution of .

Q: Find the sample standard deviation for the following Grouped Frequency Data Table (GFDT). Lower ...

A: Let x denotes the class mark, F denotes the frequency and u denotes the sample mean. Use excel to fi...