a. Find P(X = 2 ,Y<2) b. Find marginal PMF of X and Y 1 2 3 C. Find P(Y=2 |X= 1) 1/6 0 25 0 125
Q: Q = 6x + 3xy + 2y
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A: The joint distribution of X,Y is given by, f(x,y) =340<y2<x<10otherwise Note that,…
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Q: Find the value of x for which the marginal profit is zero. C(x) = 2x, R(x) = 6x - 1,000 О а. х33,000…
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Q: (6x+19)^3+30 and R(0)=0R(0
A: Application of integration: R'(x)=-36(6x+19)3+30R(0)=0Let 6x+19=z 6dx=dz
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A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…
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Q: 1. Show the marginal PDF of X. 2. Find P(X >Y). 3. Find P( < X s }).
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: (a) A manufacturer's marginal revenue function is: d = 25 – q – 0.3q³. If r is in omani rials, find…
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Q: 2) Given the joint pmff(x.y): X 0 X 5 X 6 X -1 X 2 Y=-3 0.1 0.25 0 0.2 0 Y-1 0 0.1 0.05 0 0 0.1 0.05…
A: Given Joint pmf f(x,y) as shown belowThe marginal pmfs are calculated using the formulas shown below
Q: Given a marginal p.m.f of x: f₁(x) and a marginal p.m.f of y: f₂(y) = Then the values of (k) and (c)…
A: The total probability of any probability distribution is always 1.
Q: #18 & #19
A: 18. Area under the graph is the integral of the function over the given interval.
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A: The details calculation is given below
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Q: a. What is P(X= 1 and Y= 1)? b. Compute P(X<= 1 and Y<= 1). c. Compute the marginal pmf of X and of…
A: Problem 2: a. The value of PX=1 and Y=1 is, PX=1 and Y=1=0.20 Thus, the value of PX=1 and Y=1 is…
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A: Solution
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A: It is an important part of statistics. It is widely used.
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Q: A company's marginal revenue function is MR = 190 - 16x1/3, where x is the number of units. Find the…
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Q: Find L(x). 2y – x = 3t y + a' = 3e-t x (0) = y (0) = 0 L (x): (3s+1) s? (s-2)(26+1) 3(s-1) L (x) =…
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A: Detailed explanation mentioned below
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Q: a) Find c. b) Find P(X ≤ 2Y). c) Find the marginal pdf for X and Y.
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Q: 4 Use global extrema to find constants m and M such that m < dx < M. x3-2 1.5
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Q: XIY 2 4 5 1 1/12 1/24 1/24 2 1/6 1/12 1/8 3 1/4 1/8 1/12 a. Find P(XS2,YS4) b. Find the marginal…
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Q: (a∗ ) Compute P(X = 4, Y = 5). (b∗ ) Compute the marginal pmf’s of X and Y . (c∗ ) Are X and Y…
A: The joint pmf of X and Y is given by
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- Consider a random sample X1,...,Xn,... ∼ iid Beta(θ,1) for n > 2. Prove that the MLE and UMVUE are both consistent estimators for θConsider the following two formulations of the bivariate PRF, where ui and εi are both mean-0 stochastic disturbances (i.e random errors): yi = β0 + β1xi + u yi = α0 + α1(xi − x¯) + ϵ a) Write the OLS estimators of β1 and α1. Are the two estimators the same? b) What is the advantage, if any, of the second model over the first?Show that, if X1 and X2 are independent random variables with geometric distributions of aparameter p, then Y = X1 + X2 has a negative binomial distribution with parameters p andk = 2.
- Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterIf you let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assuming the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4 and you test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi, what would be the critical region for an alpha = 0.05 significance level?
- .A sample of 9 measurements, randomly selected from a normally distributed population, resulted in x= 2.6, and s= 0.9 Conduct a hypothesis test to verify the claim that the population mean is greater than 2.5 . Use a=.05Suppose Xis a random variable with E(X) = 2, and E(X2) = 5. Compute the following quantities: a) Var(X) b) E(X−1)2 c) Var(−X−3) d) E(5X+ 4) PARTS A,B,C ARE ANSWERED ALREADY, JUST D PLEASELet X1 and X2 constitute a random sample from a nor-mal population with σ2 = 1. If the null hypothesis μ = μ0 is to be rejected in favor of the alternative hypothesis μ = μ1 > μ0 when x > μ0 + 1, what is the size of the criti-cal region?
- Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)A simple random sample of size 200 is taken from a much larger group of male wrestlers prior to a competition. The average weight in the sample is 190 pounds, with an SD of 20 pounds. The average weight of the population is estimated to be 190 pounds, and this estimate is likely to be off by about _______.
