2. The continuous random variable X has the probability density function of Jax+x Ax) = 0. otherwise 3/2 Show that a = 4 (a) Find P(0< X and give your answer in the surd form. (b) Find the median and the expected value of X.

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A: Given,f(x)=(6x-6x2)for  0&lt;x&lt;10elsewhere

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Q: Suppose X is a continuous random variable with probability density fund 0.3 0 1 f(x) = What is the…

A: The variable X is a continuous random variable.

Q: 4. The probability density function of a random variable Y is given by | 24y(10+2y-0.3y²) 0eve10…

A: From the given information, fy=24y10+2y-0.3y210000, 0&lt;y&lt;10 Consider, Ey=∫010yfydy…

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Q: 15. An insurance policy reimburses the excess of a loss over 2. The policy- holder's loss, Y,…

A: Y is denoted as the policy holder's loss. It is known, fy=2y3,if y&gt;1            0, otherwise…

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Q: Suppose that two continuous random variables X and Y have joint probability density function fxy =…

A: From the given information, Consider, Consider, EX=∫12xfxdx…

Q: with

A: Given: Computing CDF F(x) for X

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Q: Suppose that we have 2 random variables X and Y with joint probability density function fxy(x,y) = k…

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Q: Suppose that two continuous random variables X and Y have joint probability density function fry =…

A: From the given information, c.

Q: Suppose that two continuous random variables X and Y have joint probability density function fy =…

A: a. From the given information,

Q: Find the variance and standard for the continuous random variables with density functions 2x for 0 ≤…

A: List of formulae : Variance : Var(x) = E(x2)-E(x)2 Where , E(X)=∫xxf(x)dx E(X2)=∫xx2f(x)dx Standard…

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Q: Suppose that a random variable X has a continuous distribution with the probability density function…

A: Answer:-  Given X has a continuous distribution with the probability density function…

Q: 5.

A: The probability density function of the random variable Y defined by Y = log X is obtained below:Let…

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A: Given probability density function,f(x) =k(x)   for 1≤x≤50         otherwise

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A: ⇒f(x, y) = 6e-(2x +3y) ; x, y ≥ 0 Cov(x, y) = E(xy) - E(x)×E(y) E(xy) = ∫0∞∫0∞xy f(x, y)=…

Q: If the probability density function of a continuous random variable X is 0.50x 0x) = 0.4

A: Given,f(x)=0.5x   ;  0≤x≤20         ;  otherwise

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Q: Suppose that the joint density function of the random variables X and Y is      f(x,y)=k(1+2y), if…

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Q: If p(x) is a probability density function such that; The first moment EX = 0.3 and the second moment…

A: Provided information is, First moment is E(X) = 0.3 and second moment is E(X2)=2.8 Variance is…

Q: 4. Suppose that the random variable X has density function 0, fx(x) = x < 0 0 < x. 4e-4", and…

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Q: 4. Suppose that the joint distribution of X and Y can be modeled by the following probability…

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Q: Suppose that the random variable X has the probability density function | c(1– x²) for -1s x s 1…

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A: Given : f(x) = c(14 - 5x2)

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A: Solution: Let X be an exponential random variable having probability density function…

Q: 13. Suppose a continuous random variable x has the probability density Sk(1 + x), 0 1.4) using…

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

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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X +…

A: 1] X is a normal random variable 2] μ=5 and σ=1 3] Y=X2-10X+25

Q: .Let X be a random variable with the gamma probability density function. Derive the MSE of T=X² +2X

A: Here, X~Gammaθ,n,n&gt;0,θ&gt;0 and T=X2+2X