Let X, Y be discrete random variables. Sup- pose that X, Y are independent, and each has a uniform distribution over the numbers {1,2, 3}. Find Var(X – Y).

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Q: If the random variable X follows N (0, 2) and Y = 3X, find the mean and vari- %3D ance of Y.

A:

Q: Let X1,.,X, be a random sample from Normal(10,50). If Z~N(0,1) and X; (i=1,2,...,100) are…

A: The answer can be given using the concept of normal distribution.

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Q: A researcher claims that the number of homicide crimes by season is uniformly distributed. To test…

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Q: For N random variables, show that, (W,t..un) Px1..... <Ox1. x, (0,.0) =1 .......

A: Answer: For the given data,

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Q: Let x be a dis crete random variable with probability distribution fCx) =k (x² + 20) and x =…

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Q: Let X1 , X2 , X3  be  a collection of independent discrete random variables that all take the value…

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Q: Consider a random variable X~N(196,20). Find x such that Pr(X > x) = 0.293.

A: mean = 196 s = 20

Q: Let a and b be any real numbers and let x = (x,. Xz ----Lp --,L) be a data set with a sample mean f…

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Q: Let X1, X2 and X3 be independent and identically distributed random variables that follow a Poisson…

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Q: The amount of time it takes Marc to wait for the bus is continuous and uniformly distributed between…

A: Let x denote the waiting time for bus. X~U(3,14).

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: Q2) A continuous random variable has PDF Kx²+2x+1, -25xs 3. Find K, P(x)>0, X. X¹ and ².

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Q: The number of clients a store has during a week is Poisson distributed with mean A = 25. The amount…

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Q: Let X andY be independent I'(2, a)-distributed random variables. Find the conditional distribution…

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Q: Show that for two random variables X and Y, 2 2 var(aX+bY) = a¹o²+b²oy² + 2ab Cxx XY where a and b…

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Q: Exep. 2. PROve Tuat opTimaL 1 Variance V= Di bouND Saris Fies THe uppeR < min Ai V

A: To prove - Prove that optimal Variance V = 1∑i = 1k1∆i satisfies the upper bound V &lt; min1≤i≤k∆i

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Q: Find the covariance between X and Y. Please provide the solution step by step.

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Q: Show that the mean μ, median m, and variance o2 of the continuous random variable X sa - m)² ≤ 0².

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Q: Y)~ N₂(4, 5, 9, 4,-0.5). What is the conditional distribution of Y given X = 1?

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Q: Consider the following properties of independent normally distributed random variables X and Y (1)…

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Q: If x" bin(n1,p) and x2~bin(n2,p) then find the distribution of x1|x1+x2 ; where x1 and x2 are…

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Q: Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are…

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Q: Let X1, X2, andX3 be independent and normally distributed random variables with E(X1) = 4, E(X2) =…

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Q: Find the probability for P(y 3) if y is distributed as N(1, 9)

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Q: Let JO, J1,..., J4 independent random variables according to the Ber (r₁) law, where i = 0, 1,...,…

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Q: The amount of time it takes Susan to wait for the bus is continuous and uniformly distributed…

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Q: Two random variables X and Y have joint char- acteristic function rl@,a)=exp(-20,? – 8m3) Show that…

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Q: Let X have a uniform distribution on the interval (2, 9). Find the probability that the sum of 2…

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Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

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Q: Let X, X, and X, be independent random varlables having an exponential distribution with varlance…

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Q: Suppose Y is a continuous random variable drawn from the uniform distribution on the interval [3,…

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