Let f(x) is density function then

Q: Let X and Y be independent and exponential with parameter lambda. Show that the density of X…

A: Given that X and Y be independent and exponential random variables with parameter lambda.

Q: Let X and Y have the joint density function 2, 0<x<y; 0<y<1, f(x,y)= %3D 0, Otherwise. Then the…

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Q: The value of c

A: The given density function is, fx=cx2      if 0&lt;x&lt;30          otherwise It is known that the…

Q: Find the mass (in kg) of the one-dimensional object. a wire that is 5 m long (starting at x = 0) and…

A: GIVEN DATA : A one dimensional wire of Length is 5m                         Density function of wire…

Q: If the probability density of X is given by f(x)= 6x(1–x) 0<x<1 Find the probability density…

A: We know,  For any given density function. ∫-∞∞fx dx =1 Therefore, ∫016x1-x dx = 1 Let  y…

Q: e) What is the cumulative density function of X?

A: Solution-: Given: a=5, b=50 Let, X- be the waiting time for the light to turn green in seconds…

Q: Let f (2) = #{1- ()*}. 1-()}, a – B 0. Find k so that fis a density.

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Q: Find the density function of Y.

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Q: Suppose fz(z) is a function given by So23 – 2) if -<<0 fz(2) = otherwise for a fixed constant c. Can…

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Q: O Let X' and 'Y' have a joint density function 0<x< 1,0 < y< 1 other wise

A: Given information: The joint density function of the random variables X and Y is as given below:

Q: (e) Obtain the density function f(x). F(x) = F'(x) Osx < 4 otherwise (f) Calculate E(X). (9)…

A: I solved three subparts because of bartleby policy if you want more please uplode separately...

Q: Let X have the probability density f(x;0) == 20 for -0 0. Is the statistic Y = | X |, a sufficient…

A: Answer is given using concept of pdf. please find step by step solution below:

Q: Find the mass (in kg) of the one-dimensional object. a metal rod that is 6 cm long (starting at x =…

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Q: f(x, y) = ce−(2x2+6xy+3y2), −∞ < x < ∞, −∞ < y < ∞

A: Given:-   f(x,y)=ce-2x2+6xy+3y2     ,     -∞&lt;x∞,  -∞&lt;y∞   c is possitive constant.

Q: Let X and Y denote the lengths of life, in years of two components in an electronic system. If the…

A: In order to find the required probability, we will need to find the marginal density of the random…

Q: Find the density of Y = 1 – e-AX when X ~ Exp(1). Note that the density of de-dz if x > 0, f(x) =…

A: From the given information, fx=λe-λx, x&gt;0 Given that Y=1-e-λx. Consider,…

Q: Let (X,Y) have the joint density function f(x,y) = { (6/5)(1+x+y) for 0 < x, y < 1, x+y<1 otherwise…

A: From the given information, fx,y=651+x+y, 0≤x,y≤1, x+y≤1 g) Consider, fx=∫yfx,ydy…

Q: a Find the value of k that makes this a probabil- ity density function. b Find P (0.4 < X< 1). c…

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Q: Let Y possess a density function f (y) = c(2 − y),                        0 ≤ y ≤ 2,        0,…

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Q: find the density function of Z.

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Q: Is the probability density function a valid PDF? * if x 1 F(x) = x2 +=x3/2 %3D ON/30

A: the probability density function i.e., pdf of a random variable X is denoted by f(x) and the…

Q: 1. Show that the density function f(x; a, B) has a relative maximum at x = a-1 a+B-2'

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Q: Let the joint density function for Y1 and Y2 be f(y1, Y2) = 3y1, when 0<y1 <1 and 2y1 <y2 0,…

A: It is given that,fy1,y2=3y1;0&lt;y1&lt;2 and 2y1&lt;y2The magical density of 12…

Q: Is the function defined as follows a density function? fx (x) = 0 for x 4

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Q: If f(x) is density function then f(x)<0.

A: Given f(x) , a density function we need to find if given statement is true / false

Q: Let X and Y have the following joint probability density function(pdf): if 0 < x < 1, 1<y<2 f(1, y)…

A: Consider the following pdf- f(x,y)=c.x2y,0&lt;x&lt;1, 1&lt;y&lt;20,otherwise EX|Y=∫01x f(x,y)dxf(y)

Q: Find (a) Marginal density f X2 (b) Conditional density of the first, given that the second takes on…

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Q: Is the function defined as follows a density function? fx (x) = 0 for x < 2 (3 + 2x) 18 for 2 <x< 4…

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Q: If X has density f (x) = 1 – |æ| for |æ| < 1 then Var (X) =

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Q: Let fi(x) and f2(x) be two density functions on (-o, 0). Prove fi(x)log(2))dx < 0 $2(x).

A: Given See the handwritten solution

Q: E{g(X)} = [ | g(x) f. (x) dx, where f. (x) is the marginal density of X.

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Q: Find the value of C so that the function is a density function. if x < 0 f(x) = {Ce-5² if a ≥ 0.

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Q: Find a constant b > 0 so that the function e3x Sx (x) = { 4 0 < X<b elsewhere is valid density…

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Q: For variables X and Y which have joint density function given by: cy, 0<x< y < 2 0, fx,y(x, y) =…

A: Given f(x,y)=12xy,0≤x≤y≤2 (a) f(y)=∫0yf(x,y)dx      =∫0y12xydx     =12yx220y     =14y3…

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

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Q: Find E(Y/X) for the density function #(1+3y²). 0 < x < 2, 0 < y < 1 4 f (x, y) || 0, elsewhere.

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Q: Find the density of Y.

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Q: *(a) Show that E(X) = aß and V(X) = aß². %3D #(b) Suppose that a = (pdf) of Y | and let Y= (X/ß)?.…

A: Given, Therefore, a.The E(X) and V(X) are given as follows:

Q: Suppose X and Y have joint density f(x, y) = x + y 0 < x < 1,0 < y< 1. What is E(XY?)

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Q: Let X and Y have the joint density function 0<x<1; 0<y<x, 2, f(x,y)= 0, Otherwise. Calculate E(XY).

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Q: what are the necessary and sufficient conditions for a function to be of continuous density?

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Q: Let f be a GPD density function with paramters { and 3 such that -(s-1+1) f(x) = B-' (1+: where B >…

A: From the given information,

Q: Let X - Exponential (1) . Find the density of Y = 1+X'

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Q: et x and y have joint density function f(x,y) = 2e ^-x-y 0<x<y<∞ are they independent? find the…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?

A: Answer:-  Given that, X is exponentially distributed with mean 2.

Q: Suppose X has the density f (x) = (2 – x)² for 0 < x < 5.

A: Given that fx=3352-x2 0&lt;x&lt;5

Q: (a) Find the constant 'b' such that this is a valid joint density function. (b) Determine the…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.