Q8. If f(x,y) = {o (24xy, 0 sx s 1 ,0 sysi x+ys1 is a joint density function of X and Y. Find the expected value of X.

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Q: 3. The density function of X is given by f(2) = {"* + bx? 0sxs 1 otherwise If E[X] = ; find a and b.

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Q: The random varible X has density function f(x)= cxk+1(1-x)k for 00 and 1<k<2. What is mode of X?

A: This pdf is the beta first kind  We want to find the mode of beta first kind

Q: Consider the random variables with X and Y with joint density function given by ky when 0 < y < 2x <…

A: a) Given f(x,y)=ky, 0≤y≤2x≤4 ∫04∫02f(x,y)dxdy=1∫04∫02kydxdy=1k∫04y(2-0)dy=12k*y2204=116k=1k=116…

Q: 6. If the density function of X is known, the density function of Y = g(X) can be found from the CF…

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Q: Suppose the joint density function of X and Y is defined as, S(x,y) = 0sxS ys 2 Calculate the…

A: INTRODUCTION:  Conditional Probability: Let C and D are the two events. Then conditional probability…

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Q: suppose that error in the reaction temperature , in Celsius, for a controlled laboratory experiment…

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Q: The random variables X and Y have a joint density function given by S2e-2. f(x.y) = 0<x< 00, 0<y<x…

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Q: Suppose X and Y are random variables with joint density function. S0.1e-(0.5x + 0.2y) if x > 0, y >…

A: a) Given function represents the joint density for X and Y. Hence, the correct option is YEs. b)…

Q: If X is uniformly distributed over (0,1), find the density function of Y = eX

A: Solution

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Q: Let X be a random variable defined by the density function COS --4 <x5 4 fx(x) = {16 8. elsewhere…

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Q: 9. Let the distribution of X for x >0 be 3 xk e-a F(x) = 1 –E k! k=0 What is the density function of…

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Q: Let Y1 and Y2 be continuous random variables with joint density function given by fy Y2) = 0 < y2…

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Q: Let X and Y have the joint density function (x+y for 0sxS 1; 0 < ys1 elsewhere f(x, y) = Then P(2X <…

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Q: Q3- If the density function of X is (2x (x) = 0 < x < 3 %3D 0. w Find the probability mass function…

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Q: 2. find the density function with X and 0, i.e. g(x|0)

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Q: Let Y1,..., Yn denote a random sample from the density function given by fy (yl0) = ry"-le-v"10, for…

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Q: If X is uniformly distributed over (0,1), find the density function of Y = ex.

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Q: 9. Let the distribution of X for x > 0 be 3 xk e-* F(x) = 1 – ) k! k=0 What is the density function…

A: The distribution of X for x&gt;0 is given below: Fx=1-∑k=03xke-xk!

Q: m vartables A and Y has the foilowing joint probability denstty J fxy (*, y) = 2 -x- y for 0 srs1…

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Q: as the density function p(x 0.5X

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Q: A continuous random variable that can assume values between X = 2 and X 5 %3D has a density function…

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Q: Q8. If f(x,y) = (24xy, 0sxS1 ,0 <ys1 x +ys1 is a joint density function of X and Y. Find the…

A:

Q: 3. Consider the joint PDF fx(x,y) given in the following. if 0 <r<1, 0<y<1 otherwise. (a) Find the…

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Q: 4. Find the mass of a thin bar having the linear density function p(x)=6+x', defined over the range…

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Q: Q3- If the density function of X is 0 <x < 4 (x) = 38 0.w Find the probability mass function of Y =…

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Q: Suppose that for two random variables X and Y the joint density function is f(x, y) = 5xe¯x+5), for…

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Q: (d) Find the conditional density function of Y, given Y, = Y1. , where p(Y2=Y -). (Enter your…

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Q: 5. If the characteristic function of a continuous RV X with density function = S ø(@) e-ix@ dø. 2…

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Q: 10) Find the constant C > 0 so that the given function is a density of some continuous random…

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Q: 46. Given that X has a density function 2x 3 - x f (x) = for 0<x<1 and 3 for 1 Sx< 3; 3 = 0…

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Q: The two random variables and Y have the joint density function: c, 0<2y<x; 0<x<1, 0, Otherwise.…

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Q: The two random variables and Y have the joint density function: с, f(x,y)= c, 0<2y <x; 0<x<1,

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Q: - If the density function of X is (2x (x) = } 9 0 < x < 3 0. w Find the probability mass function of…

A: Given that Y=X [floor function]This means Y=0 when 0≤X&lt;11 when 1≤X&lt;22 when 2≤X&lt;3So…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!