The Pareto distribution has cdf f(x) = 1− (0/(x+0)). Suppose that a random variable X has a distribution which is a two-point mixture of two Pareto distributions, one with a = 2.5, 0 = 150, and p = 0.75, and the other with a = 6.5, 0 = 1100, and p = 0.25. Calculate the expected value of X.

Q: 5(a). The random variable X has a normal distribution with mean 11 and variance 16. Find: (i) Prob…

A: Ans#- Given, X ~ N( μ, σ2 )            Where    Mean μ = 11   and  variance σ2  = 16  ⇒   σ   = 4…

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A: Let X be a discrete random variable with PMF Px(X) , and CDF F(X), the CDF is defined as F(X) = P(X…

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Q: Find the value of the standard normal random variable z, called zo such that: (a) P(z < zo) = 0.8386…

A: As per bartleby guideline expert have to answer first question three subparts only dear student…

Q: la) P(X>2) (b) P (Y > 0), where Y = - 2

A: given  X~N5,2  the  z=X-μσ~N0, 1    mean = 5     variance = 2      ,   a) PX &gt;2=PX-μσ&gt;2-52…

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A: Let x be a Gaussian random variable,Let μμ denote the mean and σσ denote the standard deviation Let…

Q: A random variable X has the following pdf: f(x) = 9xe-3"; x > 0

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Q: If X is a binomially distributed radom variable with E(X) var (X) 4/3; find the distribution of X. 2…

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Q: Let X be a random variable with expectation E(X)=10 and variance var(X)=5. Which lower bound does…

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Q: Consider a pdf f so that a random variable X~ f has expected value E[X] = 3 and variance V[X] = 10.…

A: X~f has expected value E(X)=3  V(X)=10 We have to find Standard deviation of X- Which is larger…

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Q: f X is a uniformly distributed random varibale with a=9 and b=16, then Calculate the…

A: Answer: From the given data, X follows uniform distribution, a = 9   and   b = 16

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A: Solution: The probability mass function of random variable X is  x 2 3 4 5 Total  f(x)  0.3 0.3…

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Q: x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the…

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Q: Let B is a r.v (random variable) with Bernoulli distributionand parameter p > 0.5 . Let Var(B) =…

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Q: For an initial investment of 100, an investment yields returns of Xi at the end of period i for i =…

A: Given : μ= Population Mean =60σ2=Population Variance=25 Initial investment =100

Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: 1. Assume that Z is a standard normal random variable (i.e., it is a normal random variable with…

A: It is an important part of statistics. It is widely used.

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Q: The expected value of the transformation is 0 and the variance is 1. So if Z=0.2, when u = 3 and o =…

A: The value of Z is 0.2, mean is 3, and standard deviation is 0.2.

Q: Let w₁, W2,..., wt be independent random variables from a normal distribution with mean 0 and…

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Q: Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a]…

A: The given information is :For random variable X:Variance (Var[X]) is 4.8.For random variable…

Q: x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the…

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Q: A continuous random variable X has a PDF f(x)= 3x²,0 a} and (ii) P{X >b} = 0.05.

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Q: If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean…

A: Answer: From the given data, X follows uniform distribution, a = 8  and  b = 13

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Q: Suppose that X is a Normal random variable with E(X) = 1 and Var (X) = 1. Define Y =2X + 1. Find P(0…

A: Consider, EY=E2X+1=2EX+1∵EaX+b=aEX+b=2*1+1=3 VarY=Var2X+1=22*VarX∵VaraX+b=a2*VarX=4*1=4 SDY=VarY=4=2