Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a] How can we prove that 2X and 3Y are independent? [b] What is the standard deviation of 2X + 3Y?

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A: Z has follows standard normal distribution with mean zero and standard deviation one.

Q: How many elements does it contain?  I forgot to add that part.

A: From the above part we haven(C) = n(B) ={ (1,4),(4,1),(2,3),(3,2) }n(CB) = { (2,3),(3,2) }

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A: The data for amount of time spent on route for 40 bus drivers were given.

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A:

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A: The provided information is as follows:There are three red marbles.There are three green…

Q: Help: Suppose X ∼ Unif(a, b). Find Var(X).

A: Suppose X ∼ Unif(a, b).

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A: The random variable   represents the waiting time for the pedestrian signal. The PDF of random…

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A:

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A: X~N( μ , ?)μ=89 , ?=17Z-score =( x - μ )/?

Q: for the first part, could u tell me why the lower bound is 0 rather than x? We can see from the…

A: Expressing E(Y∣X) in terms of X:The conditional expectation of Y given X is defined as:E(Y∣X)=…

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A: It is given that for a certain population the probability that a person likes to drink coffee is…

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A: Z be the standard normal distributionP(Z<z)=0.052

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A: Let X and Y have a joint pmf

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A:

Q: Q 4.2. Let (X, Y) be a random variable with the following density: 15x²y 0 0 < x < y < 1, otherwise.…

A: Let X and Y have joint pdf

Q: 5. Suppose that E[X] = 2 and Var(X) = 6. (a) Compute E[(X + 1)²]. (b) Compute Var(4 + 3X). (c)…

A: E(X)=2, V(X)=6

Q: USE SALT are the variance and standard deviation of delay time? (Round your answers to two decimal…

A:

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A: In this first stage, the probability that an applicant is not rejected at this stage is 0.5. The…

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A: We are asked to explain and provide examples of binomial distribution in business-related or daily…

Q: Q 4.3. A fair die is rolled until a 6 is obtained. Let Y be the total number of rolls and X the…

A: Y is the total number of rolls until a 6 is obtained. This is a geometric distribution. In this…

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A: Given the probability table:Profit = $100,000Profit = $20,000Lazy / Gaming20%80%Engaged / Hard…

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A: Note: As per our guidelines we are supposed to answer only 3 sub-parts of any questions so I am…

Q: Let the probability distribution of random variable X be P(X= k) k! , k = 0, 1, 2, I then EX2 - ()

A: Let X has a pmf

Q: What is o ? XY

A: Suppose you have the following joint probability of a stock and a bond having a positive or negative…

Q: A box contains 2 red balls, 2 blue balls and 1 green ball. We draw, simultaneously without…

A: A box contains:We draw balls simultaneously, without replacement from the box.

Q: Given that is a standard normal random variable, compute the following probabilities (to 4…

A: a)P(-1.98z0.49)

Q: a) Determine the value of the normalizing constant c b) Find the MGF of the distribution of Y c)…

A:

Q: randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a…

A: Let X has a pdf

Q: Industry A is responsible for producing 60% of cements in Lebanon while Industry B produces the…

A:

Q: A car panel is spray-painted by a machine, and the technicians are particularly interested in the…

A:

Q: Consider a large-sample level 0.01 test for testing Ho: P = 0.2 against Ha: p > 0.2. USE SALT (a)…

A: Given a large-sample level 0.01 test for testing  against .

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A: From the provided information,A business organization needs to make up a 6 member fund-raising…

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A: A survey was conducted among 68 patients admitted to a hospital cardiac unit during a two-week…

Q: If a fair die is tossed once, find the probability that the uppermost face displays an even number…

A: From the provided information,A fair die is tossed once.Total outcomes = 6

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A: Here we have to identify the correct shape of Gaussian Distribution with diagonal covariance

Q: 1 f(x,y)=y The random variables X and Y have joint density function re", x>0, y>0 0, otherwise (1)…

A: Let X and Y have joint density function

Q: A random variable X has cumulative distribution function

A: A random variable X has cumulative distribution function is,

Q: Consider the following properties of a random experiment: 1. There are a fixed number of trials.…

A: We are asked to match the properties to the respective probability distributions.Properties:1. There…

Q: Q 4.1. Suppose X and Y are independent random variables, which are jointly continuous. 1. Show…

A: X and Y are independent random variables, which are jointly continuous.

Q: Assume a member is selected at random from the population represented by the graph. Find the…

A: Given:

Q: Describe the difference between odds and probability. Give an example of each to support your answer…

A: Here we have to describe the difference between odds and probability. Give an example of each to…

Q: Butch has a collection of 40 vinyl records from throughout the 20th century including seven from the…

A: The data is given as-Total number of persons = 40Number of persons in 40s = 7Number of persons in…

Q: A casino game consists of selecting two balls, without replacement, from an urn containing 7 balls…

A:

Q: 4. Let X, Y be non-negative continuous random variables with probability density functions (pdf)…

A: X and Y are independent

Q: 1. Given the directed graph as follows 1 1 201 3 2 a. Write the corresponding stochastic matrix. b.…

A: From the given directed graph, the stochastic matrix is given as:

Q: (a) Construct a CUSUM chart to analyze the data for the purpose of verifying the engineer's claim…

A: Given,ixi126.4225.3331.8427.1528.5620.2719.3822.7920.41019.51121.712241322.6(a)Define…

Q: the outcomes. 1. What is an appropriate sample space for this experiment? a. S = {AAA, N, TT, R, I,…

A: It is given that the word ANTARTICA.

Q: Q 4.2. Let (X, Y) be a random variable with the following density: 15x²y 0 0<x<y <1, otherwise.…

A: Joint pdf of X and Y is f(x,y)=15x2y; 0&lt; x&lt;y&lt;1

Q: For Question 2 Let A and B are two independent events such that P(A)=0.3 and P(B) = 0.15. Calculate…

A: P(A)=0.3 and P(B)=0.15A and B are independent.