Find the marginal densities g(x), h(y), and the conditional density f(ylx). Use f(y|x) to find P(1

Q: just f and g please

A: f)E[X] = 7/16 when x = 1, and E[X] = 9/8 when x = 2. E[Y] = 5/32 when y = 1, E[Y] = 7/16 when y = 2,…

Q: (m? +1, if m 2 Determine whether k (m)is continuous at m = 2where k (m) :

A: topic - limits and continuity k(m) is not continuous at m=2

Q: Let F(x, y, 2) = ( x+y y+z z+x 2). Is there a function f(x, y, z) such that F = Vf? If so find f,…

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Q: Consider the density function f(x) = k√√x, 0<x<1, 0. elsewhere. (a) Evaluate k. (b) Find F(x) and…

A: The PDF is given asWant to calculate the distribution function F(x)?Know that the distribution…

Q: *18. (section 3.4 ex 3.) Prove that if f(r) is continuous and f(z) = S() dt, then f(x) is…

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A: We have given that  Sample size n =254  Favorable cases x =160 Sample proportion p^=x/n  =160/254 =…

Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

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Q: How do you define local maxima, local minima, and saddle points for a differentiable function ƒ(x,…

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Q: JX,Y (2, 3 a) Find the marginal PDFs fx(x) and fy (y). b) Find the conditional PDF fyx (y|x).…

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Q: 3. Use the e, d definition to show that f(x) = x² is uniformly continuous on A = [0,3]. %3D

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Q: 0⁰ (a) Shade the area under the curve corresponding to P(13 < x < 25). 0 0⁰ 12 0⁰ 24 12 (b) Shade…

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Q: Consider two variables Y₁, Y2 whose joint probability density func- tion is given by 30y192, if y₁-1…

A: Given the joint probability density function of the random variables Y1,Y2 as fy1, y2=30y1y22,  if…

Q: .) Using the joint density directly, find E[X₁ — X₂]. i.) Using the joint density directly, find…

A: The PDF of X1,X2 is given by: fx1,x2=1x1,   0&lt;x2&lt;x1&lt;1

Q: 3. Consider the variables X and Y with the following joint probability density: f(x,y)=(2xy+x y')…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: Find the average value of the continuous function f(x) over the interval [2,5] given the following…

A: We know that average value of function f(x)  over interval [a,b] is

Q: Direction: Consider the probability density function defined by f (x) = x+5 100 1. Find P(3 < x< 5)…

A:

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1). The objective is to determine for what values of x is y undefined.…

Q: Please

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Q: 4. Let f be an integrable function on |0, 1|. a) Which of the following inequalities is true: i) f…

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Q: Let X₁, X₂, X, be distributed with pdf f(x;0)=0, 0≤x≤. 1 (c) Can you find the UMVUE of? Why? 0

A: A uniformly minimum variance unbiased estimator (UMVUE) is an unbiased estimator that, for all…

Q: Please write neatly and explain everything clearly

A: Step 1:Step 2:Step 3:Step 4:

Q: G > -A – |< :). 3 Q: Let f (y) =y² for –1 < y< 1. Find P(|Y

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Q: EXAMPLE 2 The set {sint, cost} is linearly independent in C[0, 1], the space of all continuous…

A: The given set is sin t, cos t.We need to show that the set is linearly independent.

Q: Sketch the level sets of a continuous function h(x, y) that clearly has a local maximum at (x, y) -…

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Q: The table shows selected values for a continuous functiong that is increasing over the interval [0,…

A: Consider an interval a,b and its partition a=x0&lt;x1&lt;x2&lt;⋯ &lt;xn=b. Then the integral ∫abf(x)…

Q: Find and classify the critical points of the function: f(x,y) + y² + 2xy-6x-3y + 4

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Example. Suppose the joint density of (X,Y) is Find the marginal pdf of X and Y. f(x, y) = 2,0 ≤ x,…

A: Given,f(x,y)=2  ;  0≤x,y≤1 , 0≤x+y≤1