Suppose that a pdf for a continuous random variable Y takes the form ayya-1 (1 + yª)r+1 y > 0 f() = α, γ > 0 y < 0 The median of a distribution is the value of y that solves 1 F(y) = 2 Compute the median of the distribution above if the two parameters a and y take the values 1.6 and 1.3 respectively.

Q: Q11. Let X1,X 2,.X, be a random sample from a Poisson distribution with parameter å. (a) Find the…

A: Given: X1, X2, ‐‐‐‐,Xn~Poissonλ.    ⇒fx=e-λ.λxx!   Likelihood fuction:-      ⇒Lλ =e-nλλΣxiπ x!…

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Q: We have a random variable X1 defined on Population 1.  X1 has a mean value of 52 with a population…

A: Solution: Given information: n1=625   sample size of population 1n2= 625  sample size of population…

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A: For the given random variable X, its pdf is

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Q: 6. (18 pts) Let X be a Poisson random variable with parameter λ, and Y be an independent Poisson…

A: ### Part (a): Show that λ^ is unbiasedGiven:X∼Poisson(λ)Y∼Poisson(3λ)X and Y are independent-…

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A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

A: Disclaimer "Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k

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Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

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Q: None

A: Step 1: Step 2: Step 3: Step 4:

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Q: Suppose that X has the uniform distribution on the interval [0, 1]. Compute the variance of X.

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Q: In a poisson distribution P(X=0)=P(X=2).Find the variance V(X) of X.

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