The density function of X is given by a + bæ? if 0 < x <1 f(x) %3D otherwise If the expectation of X is E(X) = 0.5, find a and b. a =

Q: Suppose f(x)=3x2, 0<x<1 is a density function of X.  Find P(1/2<X<2).

A: We have given that,  Let x is a random variable having probability density function is,  f(x) =…

Q: A random variable T has density function f(t) = kt. sin (t), 0stSA Compute E(T)

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Q: A density function f is defined by { f(x) = c(1-x) c(x-1) 0 for 0 < x < 1, for 1 < x < 2, otherwise.…

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Q: Suppose Z = X+Y. Give the probability density value at z = 0, fz(0). fx(x) fy(y) 1/2 1/2 -2 -1 y

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Q: 1. The density function of X is given by f(x)=², 1≤1≤b. == If median is e³, find a and b.

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Q: 10. A Gaussian RV X is N(0, o2-4). Find the conditional pdf: fxx>2(x); i.e., find the conditional…

A: X is a normal distribution with mean 0 and variance 4 X ~ N(0,σ2 =4) So,  Z = X-04=X2 ~ N(0,1) CDF…

Q: Let X be a continuous random variable with a density function fX (x) = (c sin (πx)   0 <x <1…

A: solution:-given x be a continuous ranom variable with density functionf(x)=sin(π),0&lt;x&lt;10…

Q: Find the value of k that makes the function f (x, y)=ke²x-³y a joint probability density function…

A: f(x,y)=ke2x-3y ; x&gt;0, y&gt;x

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: I need answer with explaination

A: Given the stop loss premium πx(d) = E[(X-d)+] = 132-d3 d∈[1,2]

Q: Find the value of k that makes the function f (x, y)=ke-²x-³y a joint probability density function…

A: Given density function, fx,y=ke-2x-3y, 0&lt;x and x&lt;y         =ke-2x-3y, 0&lt;x &lt;y,…

Q: Find E(X)

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Q: Let random variable X have the density function: cx² + x, 0<x<1, f(x)%3= 0, otherwise. Find the…

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Q: (c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1, 2, the waiting…

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Q: X ∼ U[0, 1] has a uniform distribution. Y = eX + 1 It is defined as. Specify the domain of X. Draw…

A: INTRODUCTION :  UNIFORM DISTRIBUTION:  A continuous random variable X is said to follow UNIFORM…

Q: i. the value of the constant C. ii. the marginal probability density functions of fx(x) of X and…

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Q: Q6. Consider the probability density function fex) = {C A if x>1 Inx %3D X2 otherwise . Ca) Find C.…

A: Given function f(x)=clnxx2if x≥100therwise find c find Px≥3

Q: Find the value of k that makes the function f (x, y) =15e-2x-3y a joint probability density function…

A: As per our guidelines I can solve only first three subparts. Kindly post the remaining subpart again…

Q: 1) Show that the given function is a pdf (Probability Density Function) Q6 f(x) = = e7, [0, In4]

A: The probability density function is ∫-∞∞f(x)dx=1 if Pa≤x≤b=∫abf(x)dx and f(x)≥0 if the function is a…

Q: (b) Suppose X and Y are random variables with joint density function fxy(x, y) = 3x, 0<y<x< 1. i.…

A: To solve this problem, we'll go through each part step by step.i. To find the conditional density…

Q: Suppose the density function of Y is defined as, 3 s(9) = (1- y²), 0sysı Calculate expectation of Y.…

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Q: b) Find the marginal probability density function of Y, fy (y).

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Q: Determine K and the distribution function.

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Q: Find the density of Z = X − Y for independent Exp(λ) random variables X and

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Q: c) If we have the following density function: f(x) = cx, 0<x< 2: Find 1. C 2. V(x) 3. F(x)

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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: The density function of X is given by If the expectation of X is E(X) = 0.5625, find a and b. a 15 b…

A: Given the density function of X is,And E(X) = 0.5625

Q: In a certain community, levels of air pollution may exceed federal standards for ozone or for…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: If x has a uniform density with a=-2 and b=5. Let y=|x|. Find the probability density function of y…

A: We have given that the random variable X has a uniform density with a=-2 and b=5.   The pdf of…

Q: Find the cumulative distribution function for Y if its density is f(y) = { 0, S 2(1 – 1/y²), 1 1.5).

A: Solution: From the given information, the probability density function of Y is

Q: The density function of X is:  f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

A: The density function of X is: f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

Q: If f(x)= O<x<5 is a probability density function and m is unknown real number (constant), then m=

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Q: X ∼ U [0, 1] has a uniform distribution. It is defined as Y = e ^ x 1. Indicate the domain of X.…

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Q: Let X have the density function x >0, e f(x) = 0, Otherwise. Then the expected value of 3

A: The probability density function for X is,

Q: Suppose Y is a continuous random variable with density function (c(2y + -1sys5 elsewhere %3D 0, Find…

A: Probability density function

Q: The density function of X is given by ļ a + bx? if 0 < x < 1 f(x) = otherwise If the expectation of…

A: Given that the density function of X is fx=a+bx2         if   0≤x≤10                   otherwise And…

Q: Find the distribution function and density function of Y = sinX, where X is distributed uniformly…

A: Solution-: Find the distribution function and density function of Y = sinX, where X is distributed…

Q: 5. Given the density function of X as fx (x) = e iu (x), and T (X) = XI, then f, (y) is O eu (y)

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Q: fx(x) = (2) c² (0.95)³-²1{1,2,3,4,5) (2) a. с fx(x) = 2x +4¹(0-2)(x) b.

A: Solution

Q: a. What is a? b. What is E(X)? C. What is Var(X)?

A: Here given probability density function of random variable.

Q: At a restaurant, the density function for the time a customer has to wait before being seated is…

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Q: The conditional probability density function of Y, given that X=x for some x>0, takes the following…

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Q: Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes…

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